Geometry Regents at Random Worksheets - JMap
Geometry Regents at Random Worksheets - JMap
Geometry Regents at Random Worksheets - JMap
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<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 1 NAME:________________________________<br />
www.jmap.org<br />
<strong>Geometry</strong> <strong>Regents</strong> <strong>at</strong> <strong>Random</strong> <strong>Worksheets</strong><br />
1 Solve the following system of equ<strong>at</strong>ions<br />
graphically.<br />
2x 2 − 4x = y + 1<br />
x + y = 1<br />
2 In circle O, a diameter has endpoints (−5,4) and<br />
(3,−6). Wh<strong>at</strong> is the length of the diameter?<br />
1) 2<br />
2) 2 2<br />
3) 10<br />
4) 2 41<br />
3 Which st<strong>at</strong>ement is the neg<strong>at</strong>ion of “Two is a prime<br />
number” and wh<strong>at</strong> is the truth value of the<br />
neg<strong>at</strong>ion?<br />
1) Two is not a prime number; false<br />
2) Two is not a prime number; true<br />
3) A prime number is two; false<br />
4) A prime number is two; true<br />
4 In DEF, m∠D = 3x + 5, m∠E = 4x − 15, and<br />
m∠F = 2x + 10. Which st<strong>at</strong>ement is true?<br />
1) DF = FE<br />
2) DE = FE<br />
3) m∠E = m∠F<br />
4) m∠D = m∠F<br />
5 In the diagram below of quadril<strong>at</strong>eral ABCD,<br />
AD ≅ BC and ∠DAE ≅ ∠BCE. Line segments<br />
AC, DB, and FG intersect <strong>at</strong> E.<br />
Prove: AEF ≅ CEG<br />
6 The volume of a rectangular prism is 144 cubic<br />
inches. The height of the prism is 8 inches. Which<br />
measurements, in inches, could be the dimensions<br />
of the base?<br />
1) 3.3 by 5.5<br />
2) 2.5 by 7.2<br />
3) 12 by 8<br />
4) 9 by 9
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 2 NAME:________________________________<br />
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7 In the diagram below of ACD, B is a point on<br />
AC such th<strong>at</strong> ADB is an equil<strong>at</strong>eral triangle, and<br />
DBC is an isosceles triangle with DB ≅ BC .<br />
Find m∠C.<br />
8 As shown on the graph below, R′S ′T ′ is the<br />
image of RST under a single transform<strong>at</strong>ion.<br />
Which transform<strong>at</strong>ion does this graph represent?<br />
1) glide reflection<br />
2) line reflection<br />
3) rot<strong>at</strong>ion<br />
4) transl<strong>at</strong>ion<br />
9 The diagram below shows a rectangular prism.<br />
Which pair of edges are segments of lines th<strong>at</strong> are<br />
coplanar?<br />
1) AB and DH<br />
2) AE and DC<br />
3) BC and EH<br />
4) CG and EF<br />
10 .A straightedge and compass were used to cre<strong>at</strong>e<br />
the construction below. Arc EF was drawn from<br />
point B, and arcs with equal radii were drawn from<br />
E and F.<br />
Which st<strong>at</strong>ement is false?<br />
1) m∠ABD = m∠DBC<br />
2)<br />
1<br />
(m∠ABC) = m∠ABD<br />
2<br />
3) 2(m∠DBC) = m∠ABC<br />
4) 2(m∠ABC) = m∠CBD
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 3 NAME:________________________________<br />
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11 Which graph represents a circle whose equ<strong>at</strong>ion is<br />
(x + 2) 2 + y 2 = 16?<br />
1)<br />
2)<br />
3)<br />
4)<br />
12 In the diagram below of ABC, D is a point on<br />
AB, E is a point on BC , AC DE, CE = 25 inches,<br />
AD = 18 inches, and DB = 12 inches. Find, to the<br />
nearest tenth of an inch, the length of EB.<br />
13 Using a compass and straightedge, construct a line<br />
perpendicular to AB through point P. [Leave all<br />
construction marks.]
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 4 NAME:________________________________<br />
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14 Which line is parallel to the line whose equ<strong>at</strong>ion is<br />
4x + 3y = 7 and also passes through the point<br />
(−5,2)?<br />
1) 4x + 3y = −26<br />
2) 4x + 3y = −14<br />
3) 3x + 4y = −7<br />
4) 3x + 4y = 14<br />
15 The cylindrical tank shown in the diagram below is<br />
to be painted. The tank is open <strong>at</strong> the top, and the<br />
bottom does not need to be painted. Only the<br />
outside needs to be painted. Each can of paint<br />
covers 600 square feet. How many cans of paint<br />
must be purchased to complete the job?<br />
16 Which equ<strong>at</strong>ion represents the perpendicular<br />
bisector of AB whose endpoints are A(8,2) and<br />
B(0,6)?<br />
1) y = 2x − 4<br />
2) y = − 1<br />
x + 2<br />
2<br />
3) y = − 1<br />
x + 6<br />
2<br />
4) y = 2x − 12<br />
17 Wh<strong>at</strong> is the equ<strong>at</strong>ion of the line th<strong>at</strong> passes through<br />
the point (−9,6) and is perpendicular to the line<br />
y = 3x − 5?<br />
1) y = 3x + 21<br />
2) y = − 1<br />
x − 3<br />
3<br />
3) y = 3x + 33<br />
4) y = − 1<br />
x + 3<br />
3<br />
18 Triangle ABC has vertices A(−2,2), B(−1,−3), and<br />
C(4,0). Find the coordin<strong>at</strong>es of the vertices of<br />
A′B′C ′, the image of ABC after the<br />
transform<strong>at</strong>ion r x-axis . [The use of the grid is<br />
optional.]
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 5 NAME:________________________________<br />
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19 In the diagram below, line p intersects line m and<br />
line n.<br />
If m∠1 = 7x and m∠2 = 5x + 30, lines m and n are<br />
parallel when x equals<br />
1) 12.5<br />
2) 15<br />
3) 87.5<br />
4) 105<br />
20 Find, in degrees, the measures of both an interior<br />
angle and an exterior angle of a regular pentagon.<br />
21 In the diagram below, ABC ≅ XYZ.<br />
Which st<strong>at</strong>ement must be true?<br />
1) ∠C ≅ ∠Y<br />
2) ∠A ≅ ∠X<br />
3) AC ≅ YZ<br />
4) CB ≅ XZ<br />
22 Given th<strong>at</strong> ABCD is a parallelogram, a student<br />
wrote the proof below to show th<strong>at</strong> a pair of its<br />
opposite angles are congruent.<br />
Wh<strong>at</strong> is the reason justifying th<strong>at</strong> ∠B ≅ ∠D?<br />
1) Opposite angles in a quadril<strong>at</strong>eral are<br />
congruent.<br />
2) Parallel lines have congruent corresponding<br />
angles.<br />
3) Corresponding parts of congruent triangles are<br />
congruent.<br />
4) Altern<strong>at</strong>e interior angles in congruent triangles<br />
are congruent.<br />
23 In the diagram below of ADE, B is a point on AE<br />
and C is a point on AD such th<strong>at</strong> BC ED,<br />
AC = x − 3, BE = 20, AB = 16, and AD = 2x + 2.<br />
Find the length of AC.
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 6 NAME:________________________________<br />
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24 On the diagram below, use a compass and<br />
straightedge to construct the bisector of ∠ABC.<br />
[Leave all construction marks.]<br />
25 The coordin<strong>at</strong>es of trapezoid ABCD are A(−4,5),<br />
B(1,5), C(1,2), and D(−6,2). Trapezoid<br />
A″B″C ″D″ is the image after the composition<br />
r x − axis r y = x is performed on trapezoid ABCD.<br />
St<strong>at</strong>e the coordin<strong>at</strong>es of trapezoid A″B″C ″D″.<br />
[The use of the set of axes below is optional.]<br />
26 For which polygon does the sum of the measures of<br />
the interior angles equal the sum of the measures of<br />
the exterior angles?<br />
1) hexagon<br />
2) pentagon<br />
3) quadril<strong>at</strong>eral<br />
4) triangle<br />
27 In the diagram below, ABC ∼ DEF, DE = 4,<br />
AB = x, AC = x + 2, and DF = x + 6. Determine the<br />
length of AB. [Only an algebraic solution can<br />
receive full credit.]<br />
28 Point M is the midpoint of AB. If the coordin<strong>at</strong>es<br />
of A are (−3,6) and the coordin<strong>at</strong>es of M are (−5,2),<br />
wh<strong>at</strong> are the coordin<strong>at</strong>es of B?<br />
1) (1,2)<br />
2) (7,10)<br />
3) (−4,4)<br />
4) (−7,−2)<br />
29 Which st<strong>at</strong>ement is true about every parallelogram?<br />
1) All four sides are congruent.<br />
2) The interior angles are all congruent.<br />
3) Two pairs of opposite sides are congruent.<br />
4) The diagonals are perpendicular to each other.
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 7 NAME:________________________________<br />
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30 Which graph represents a circle with the equ<strong>at</strong>ion<br />
(x − 3) 2 + (y + 1) 2 = 4?<br />
1)<br />
2)<br />
3)<br />
4)<br />
31 In the diagram below, BFCE, AB ⊥ BE ,<br />
DE ⊥ BE , and ∠BFD ≅ ∠ECA. Prove th<strong>at</strong><br />
ABC ∼ DEF.<br />
32 In the diagram below, point M is loc<strong>at</strong>ed on AB → ←⎯<br />
.<br />
Sketch the locus of points th<strong>at</strong> are 1 unit from AB → ←⎯<br />
and the locus of points 2 units from point M. Label<br />
with an X all points th<strong>at</strong> s<strong>at</strong>isfy both conditions.<br />
33 For a triangle, which two points of concurrence<br />
could be loc<strong>at</strong>ed outside the triangle?<br />
1) incenter and centroid<br />
2) centroid and orthocenter<br />
3) incenter and circumcenter<br />
4) circumcenter and orthocenter
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 8 NAME:________________________________<br />
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34 In the diagram below of ABC, D is the midpoint<br />
of AB, and E is the midpoint of BC .<br />
If AC = 4x + 10, which expression represents DE?<br />
1) x + 2.5<br />
2) 2x + 5<br />
3) 2x + 10<br />
4) 8x + 20<br />
35 In the diagram below, parallelogram ABCD has<br />
diagonals AC and BD th<strong>at</strong> intersect <strong>at</strong> point E.<br />
Which expression is not always true?<br />
1) ∠DAE ≅ ∠BCE<br />
2) ∠DEC ≅ ∠BEA<br />
3) AC ≅ DB<br />
4) DE ≅ EB<br />
36 Wh<strong>at</strong> is an equ<strong>at</strong>ion of the line th<strong>at</strong> passes through<br />
the point (−2,3) and is parallel to the line whose<br />
equ<strong>at</strong>ion is y = 3<br />
x − 4?<br />
2<br />
1) y = −2<br />
3 x<br />
2) y = −2<br />
3<br />
3) y = 3<br />
2 x<br />
x + 5<br />
3<br />
4) y = 3<br />
x + 6<br />
2<br />
37 If two distinct planes, A and B, are perpendicular<br />
to line c, then which st<strong>at</strong>ement is true?<br />
1) Planes A and B are parallel to each other.<br />
2) Planes A and B are perpendicular to each<br />
other.<br />
3) The intersection of planes A and B is a line<br />
parallel to line c.<br />
4) The intersection of planes A and B is a line<br />
perpendicular to line c.<br />
38 A student wrote the sentence “4 is an odd integer.”<br />
Wh<strong>at</strong> is the neg<strong>at</strong>ion of this sentence and the truth<br />
value of the neg<strong>at</strong>ion?<br />
1) 3 is an odd integer; true<br />
2) 4 is not an odd integer; true<br />
3) 4 is not an even integer; false<br />
4) 4 is an even integer; false
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 9 NAME:________________________________<br />
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39 In the diagram below of circle O, radius OC is 5<br />
cm. Chord AB is 8 cm and is perpendicular to OC<br />
<strong>at</strong> point P.<br />
Wh<strong>at</strong> is the length of OP, in centimeters?<br />
1) 8<br />
2) 2<br />
3) 3<br />
4) 4<br />
40 In the diagram below, LATE is an isosceles<br />
trapezoid with LE ≅ AT, LA = 24, ET = 40, and<br />
AT = 10. Altitudes LF and AG are drawn.<br />
Wh<strong>at</strong> is the length of LF?<br />
1) 6<br />
2) 8<br />
3) 3<br />
4) 4<br />
41 Segment AB is the diameter of circle M. The<br />
coordin<strong>at</strong>es of A are (−4,3). The coordin<strong>at</strong>es of M<br />
are (1,5). Wh<strong>at</strong> are the coordin<strong>at</strong>es of B?<br />
1) (6,7)<br />
2) (5,8)<br />
3) (−3,8)<br />
4) (−5,2)<br />
42 Using a compass and straightedge, construct the<br />
bisector of ∠CBA. [Leave all construction marks.]<br />
43 In the diagram below of ABC, side BC is<br />
extended to point D, m∠A = x, m∠B = 2x + 15, and<br />
m∠ACD = 5x + 5.<br />
Wh<strong>at</strong> is m∠B?<br />
1) 5<br />
2) 20<br />
3) 25<br />
4) 55
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 10 NAME:________________________________<br />
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44 On the set of coordin<strong>at</strong>e axes below, graph the<br />
locus of points th<strong>at</strong> are equidistant from the lines<br />
y = 6 and y = 2 and also graph the locus of points<br />
th<strong>at</strong> are 3 units from the y-axis. St<strong>at</strong>e the<br />
coordin<strong>at</strong>es of all points th<strong>at</strong> s<strong>at</strong>isfy both<br />
conditions.<br />
45 Wh<strong>at</strong> is the slope of a line th<strong>at</strong> is perpendicular to<br />
the line represented by the equ<strong>at</strong>ion x + 2y = 3?<br />
1) −2<br />
2) 2<br />
3) − 1<br />
4)<br />
1<br />
2<br />
2<br />
46 Wh<strong>at</strong> is the measure of each interior angle of a<br />
regular hexagon?<br />
1) 60°<br />
2) 120°<br />
3) 135°<br />
4) 270°<br />
47 The angles of triangle ABC are in the r<strong>at</strong>io of<br />
8:3:4. Wh<strong>at</strong> is the measure of the smallest angle?<br />
1) 12º<br />
2) 24º<br />
3) 36º<br />
4) 72º<br />
48 Chords AB and CD intersect <strong>at</strong> E in circle O, as<br />
shown in the diagram below. Secant FDA and<br />
tangent FB are drawn to circle O from external<br />
point F and chord AC is drawn. The mDA = 56,<br />
mDB = 112, and the r<strong>at</strong>io of mAC :mCB = 3:1.<br />
Determine m∠CEB. Determine m∠F . Determine<br />
m∠DAC .<br />
49 A paint can is in the shape of a right circular<br />
cylinder. The volume of the paint can is 600<br />
cubic inches and its altitude is 12 inches. Find the<br />
radius, in inches, of the base of the paint can.<br />
Express the answer in simplest radical form. Find,<br />
to the nearest tenth of a square inch, the l<strong>at</strong>eral<br />
area of the paint can.
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 11 NAME:________________________________<br />
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50 In the diagram below of GJK, H is a point on<br />
GJ , HJ ≅ JK , m∠G = 28, and m∠GJK = 70.<br />
Determine whether GHK is an isosceles triangle<br />
and justify your answer.<br />
51 Pentagon PQRST has PQ parallel to TS. After a<br />
transl<strong>at</strong>ion of T 2,−5 , which line segment is parallel<br />
to P ′Q′?<br />
1) R′Q′<br />
2) R′S ′<br />
3) T ′S ′<br />
4) T ′P′<br />
52 In ABC and DEF, AC CB<br />
= . Which<br />
DF FE<br />
additional inform<strong>at</strong>ion would prove<br />
ABC ∼ DEF?<br />
1) AC = DF<br />
2) CB = FE<br />
3) ∠ACB ≅ ∠DFE<br />
4) ∠BAC ≅ ∠EDF<br />
53 Wh<strong>at</strong> is the image of the point (2,−3) after the<br />
transform<strong>at</strong>ion r y − axis ?<br />
1) (2,3)<br />
2) (−2,−3)<br />
3) (−2,3)<br />
4) (−3,2)<br />
54 Write the neg<strong>at</strong>ion of the st<strong>at</strong>ement “2 is a prime<br />
number,” and determine the truth value of the<br />
neg<strong>at</strong>ion.<br />
55 Given three distinct quadril<strong>at</strong>erals, a square, a<br />
rectangle, and a rhombus, which quadril<strong>at</strong>erals<br />
must have perpendicular diagonals?<br />
1) the rhombus, only<br />
2) the rectangle and the square<br />
3) the rhombus and the square<br />
4) the rectangle, the rhombus, and the square<br />
56 On the diagram of ABC shown below, use a<br />
compass and straightedge to construct the<br />
perpendicular bisector of AC. [Leave all<br />
construction marks.]
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 12 NAME:________________________________<br />
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57 A man wants to place a new bird b<strong>at</strong>h in his yard so<br />
th<strong>at</strong> it is 30 feet from a fence, f, and also 10 feet<br />
from a light pole, P. As shown in the diagram<br />
below, the light pole is 35 feet away from the<br />
fence.<br />
How many loc<strong>at</strong>ions are possible for the bird b<strong>at</strong>h?<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 0<br />
58 As shown in the diagram below, AC bisects ∠BAD<br />
and ∠B ≅ ∠D.<br />
Which method could be used to prove<br />
ABC ≅ ADC?<br />
1) SSS<br />
2) AAA<br />
3) SAS<br />
4) AAS<br />
59 In the diagram below of circle O, chord AB is<br />
parallel to chord GH . Chord CD intersects AB <strong>at</strong><br />
E and GH <strong>at</strong> F.<br />
Which st<strong>at</strong>ement must always be true?<br />
1) AC ≅ CB<br />
2) DH ≅ BH<br />
3) AB ≅ GH<br />
4) AG ≅ BH<br />
60 The coordin<strong>at</strong>es of the endpoints of FG are (−4,3)<br />
and (2,5). Find the length of FG in simplest<br />
radical form.<br />
61 In FGH , m∠F = 42 and an exterior angle <strong>at</strong><br />
vertex H has a measure of 104. Wh<strong>at</strong> is m∠G?<br />
1) 34<br />
2) 62<br />
3) 76<br />
4) 146
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 13 NAME:________________________________<br />
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62 The coordin<strong>at</strong>es of point A are (−3a,4b). If point<br />
A' is the image of point A reflected over the line<br />
y = x, the coordin<strong>at</strong>es of A' are<br />
1) (4b,−3a)<br />
2) (3a,4b)<br />
3) (−3a,−4b)<br />
4) (−4b,−3a)<br />
63 A line segment has endpoints A(7,−1) and B(−3,3).<br />
Wh<strong>at</strong> are the coordin<strong>at</strong>es of the midpoint of AB?<br />
1) (1,2)<br />
2) <br />
<br />
2,1<br />
<br />
<br />
3) (−5,2)<br />
4) <br />
<br />
5,−2<br />
<br />
64 Plane A is parallel to plane B. Plane C intersects<br />
plane A in line m and intersects plane B in line n.<br />
Lines m and n are<br />
1) intersecting<br />
2) parallel<br />
3) perpendicular<br />
4) skew<br />
65 Which equ<strong>at</strong>ion represents circle O with center<br />
(2,−8) and radius 9?<br />
1) (x + 2) 2 + (y − 8) 2 = 9<br />
2) (x − 2) 2 + (y + 8) 2 = 9<br />
3) (x + 2) 2 + (y − 8) 2 = 81<br />
4) (x − 2) 2 + (y + 8) 2 = 81<br />
66 Which diagram shows the construction of the<br />
perpendicular bisector of AB?<br />
1)<br />
2)<br />
3)<br />
4)
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 14 NAME:________________________________<br />
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67 In the diagram below, AB → ←⎯<br />
AEFG.<br />
is perpendicular to plane<br />
Which plane must be perpendicular to plane<br />
AEFG?<br />
1) ABCE<br />
2) BCDH<br />
3) CDFE<br />
4) HDFG<br />
68 The sum of the interior angles of a polygon of n<br />
sides is<br />
1) 360<br />
2)<br />
360<br />
n<br />
3) (n − 2) ⋅ 180<br />
4)<br />
(n − 2) ⋅ 180<br />
n<br />
69 If JKL ≅ MNO, which st<strong>at</strong>ement is always<br />
true?<br />
1) ∠KLJ ≅ ∠NMO<br />
2) ∠KJL ≅ ∠MON<br />
3) JL ≅ MO<br />
4) JK ≅ ON<br />
70 In the diagram below, m and QR⊥ ST <strong>at</strong> R.<br />
If m∠1 = 63, find m∠2.<br />
71 The coordin<strong>at</strong>es of the endpoints of AB are A(0,0)<br />
and B(0,6). The equ<strong>at</strong>ion of the perpendicular<br />
bisector of AB is<br />
1) x = 0<br />
2) x = 3<br />
3) y = 0<br />
4) y = 3<br />
72 In the diagram below of right triangle ABC, CD is<br />
the altitude to hypotenuse AB, CB = 6, and AD = 5.<br />
Wh<strong>at</strong> is the length of BD?<br />
1) 5<br />
2) 9<br />
3) 3<br />
4) 4
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 15 NAME:________________________________<br />
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73 In the diagram below of BCD, side DB is<br />
extended to point A.<br />
Which st<strong>at</strong>ement must be true?<br />
1) m∠C > m∠D<br />
2) m∠ABC < m∠D<br />
3) m∠ABC > m∠C<br />
4) m∠ABC > m∠C + m∠D<br />
74 The st<strong>at</strong>ement "x is a multiple of 3, and x is an even<br />
integer" is true when x is equal to<br />
1) 9<br />
2) 8<br />
3) 3<br />
4) 6<br />
75 The point (3,−2) is rot<strong>at</strong>ed 90º about the origin and<br />
then dil<strong>at</strong>ed by a scale factor of 4. Wh<strong>at</strong> are the<br />
coordin<strong>at</strong>es of the resulting image?<br />
1) (−12,8)<br />
2) (12,-8)<br />
3) (8,12)<br />
4) (−8,−12)<br />
76 Wh<strong>at</strong> is the image of the point (−5,2) under the<br />
transl<strong>at</strong>ion T 3,−4 ?<br />
1) (−9,5)<br />
2) (−8,6)<br />
3) (−2,−2)<br />
4) (−15,−8)<br />
77 Triangle ABC has vertices A(3,3), B(7,9), and<br />
C(11,3). Determine the point of intersection of the<br />
medians, and st<strong>at</strong>e its coordin<strong>at</strong>es. [The use of the<br />
set of axes below is optional.]<br />
78 A sphere has a diameter of 18 meters. Find the<br />
volume of the sphere, in cubic meters, in terms of<br />
π .<br />
79 The Parkside Packing Company needs a<br />
rectangular shipping box. The box must have a<br />
length of 11 inches and a width of 8 inches. Find,<br />
to the nearest tenth of an inch, the minimum height<br />
of the box such th<strong>at</strong> the volume is <strong>at</strong> least 800<br />
cubic inches.
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80 In the diagram below of circle O, diameter AB is<br />
parallel to chord CD.<br />
If mCD = 70, wh<strong>at</strong> is mAC ?<br />
1) 110<br />
2) 70<br />
3) 55<br />
4) 35<br />
81 In the diagram below of circle O, diameter AOB is<br />
perpendicular to chord CD <strong>at</strong> point E, OA = 6, and<br />
OE = 2.<br />
Wh<strong>at</strong> is the length of CE?<br />
1) 4 3<br />
2) 2 3<br />
3) 8 2<br />
4) 4 2<br />
82 Which diagram represents a correct construction of<br />
equil<strong>at</strong>eral ABC, given side AB?<br />
1)<br />
2)<br />
3)<br />
4)
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83 In scalene triangle ABC, m∠B = 45 and m∠C = 55.<br />
Wh<strong>at</strong> is the order of the sides in length, from<br />
longest to shortest?<br />
1) AB, BC , AC<br />
2) BC , AC, AB<br />
3) AC, BC , AB<br />
4) BC , AB, AC<br />
84 Wh<strong>at</strong> is the equ<strong>at</strong>ion of a line passing through<br />
(2,−1) and parallel to the line represented by the<br />
equ<strong>at</strong>ion y = 2x + 1?<br />
1) y = − 1<br />
2 x<br />
2) y = − 1<br />
x + 1<br />
2<br />
3) y = 2x − 5<br />
4) y = 2x − 1<br />
85 In the diagram of quadril<strong>at</strong>eral ABCD, AB CD,<br />
∠ABC ≅ ∠CDA, and diagonal AC is drawn.<br />
Which method can be used to prove ABC is<br />
congruent to CDA?<br />
1) AAS<br />
2) SSA<br />
3) SAS<br />
4) SSS<br />
86 The vertices of parallelogram ABCD are A(2,0),<br />
B(0,−3), C(3,−3), and D(5,0). If ABCD is<br />
reflected over the x-axis, how many vertices remain<br />
invariant?<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 0<br />
87 Line segment AB is shown in the diagram below.<br />
Which two sets of construction marks, labeled I, II,<br />
III, and IV, are part of the construction of the<br />
perpendicular bisector of line segment AB?<br />
1) I and II<br />
2) I and III<br />
3) II and III<br />
4) II and IV<br />
88 Lines a and b intersect <strong>at</strong> point P. Line c passes<br />
through P and is perpendicular to the plane<br />
containing lines a and b. Which st<strong>at</strong>ement must be<br />
true?<br />
1) Lines a, b, and c are coplanar.<br />
2) Line a is perpendicular to line b.<br />
3) Line c is perpendicular to both line a and line<br />
b.<br />
4) Line c is perpendicular to line a or line b, but<br />
not both.
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89 In the diagram below, ABC ∼ RST.<br />
Which st<strong>at</strong>ement is not true?<br />
1) ∠A ≅ ∠R<br />
2)<br />
AB BC<br />
=<br />
RS ST<br />
3)<br />
AB ST<br />
=<br />
BC RS<br />
4)<br />
AB + BC + AC AB<br />
=<br />
RS + ST + RT RS<br />
90 A pentagon is drawn on the set of axes below. If<br />
the pentagon is reflected over the y-axis, determine<br />
if this transform<strong>at</strong>ion is an isometry. Justify your<br />
answer. [The use of the set of axes is optional.]<br />
91 When a quadril<strong>at</strong>eral is reflected over the line<br />
y = x, which geometric rel<strong>at</strong>ionship is not<br />
preserved?<br />
1) congruence<br />
2) orient<strong>at</strong>ion<br />
3) parallelism<br />
4) perpendicularity<br />
92 Which equ<strong>at</strong>ion represents the line parallel to the<br />
line whose equ<strong>at</strong>ion is 4x + 2y = 14 and passing<br />
through the point (2,2)?<br />
1) y = −2x<br />
2) y = −2x + 6<br />
3) y = 1<br />
2 x<br />
4) y = 1<br />
x + 1<br />
2<br />
93 In the diagram below, LMO is isosceles with<br />
LO = MO.<br />
If m∠L = 55 and m∠NOM = 28, wh<strong>at</strong> is m∠N ?<br />
1) 27<br />
2) 28<br />
3) 42<br />
4) 70
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94 On the diagram below, use a compass and<br />
straightedge to construct the bisector of ∠XYZ.<br />
[Leave all construction marks.]<br />
95 In the diagram below, trapezoid ABCD, with bases<br />
AB and DC , is inscribed in circle O, with diameter<br />
DC . If mAB=80, find mBC .<br />
96 In the diagram below of ABCD, AC ≅ BD.<br />
Using this inform<strong>at</strong>ion, it could be proven th<strong>at</strong><br />
1) BC = AB<br />
2) AB = CD<br />
3) AD − BC = CD<br />
4) AB + CD = AD<br />
97 In a given triangle, the point of intersection of the<br />
three medians is the same as the point of<br />
intersection of the three altitudes. Which<br />
classific<strong>at</strong>ion of the triangle is correct?<br />
1) scalene triangle<br />
2) isosceles triangle<br />
3) equil<strong>at</strong>eral triangle<br />
4) right isosceles triangle<br />
98 In the diagram below, quadril<strong>at</strong>eral JUMP is<br />
inscribed in a circle..<br />
Opposite angles J and M must be<br />
1) right<br />
2) complementary<br />
3) congruent<br />
4) supplementary
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99 Which equ<strong>at</strong>ion represents a line th<strong>at</strong> is parallel to<br />
the line whose equ<strong>at</strong>ion is y = 3<br />
x − 3 and passes<br />
2<br />
through the point (1,2)?<br />
1) y = 3 1<br />
x +<br />
2 2<br />
2) y = 2 4<br />
x +<br />
3 3<br />
3) y = 3<br />
x − 2<br />
2<br />
4) y = − 2 8<br />
x +<br />
3 3<br />
100 As shown in the diagram below of ABC, a<br />
compass is used to find points D and E, equidistant<br />
from point A. Next, the compass is used to find<br />
point F, equidistant from points D and E. Finally, a<br />
straightedge is used to draw AF → ⎯⎯<br />
. Then, point G,<br />
the intersection of AF → ⎯⎯<br />
and side BC of ABC, is<br />
labeled.<br />
Which st<strong>at</strong>ement must be true?<br />
1) AF → ⎯⎯<br />
⎯⎯<br />
2)<br />
bisects side BC<br />
AF →<br />
bisects ∠BAC<br />
3) AF → ⎯⎯<br />
⊥ BC<br />
4) ABG ∼ ACG<br />
101 As shown in the diagram below, EF → ←⎯⎯<br />
planes P, Q, and R.<br />
If EF → ←⎯⎯<br />
intersects<br />
is perpendicular to planes P and R, which<br />
st<strong>at</strong>ement must be true?<br />
1) Plane P is perpendicular to plane Q.<br />
2) Plane R is perpendicular to plane P.<br />
3) Plane P is parallel to plane Q.<br />
4) Plane R is parallel to plane P.<br />
102 Wh<strong>at</strong> is an equ<strong>at</strong>ion of the line th<strong>at</strong> is perpendicular<br />
to the line whose equ<strong>at</strong>ion is y = 3<br />
x − 2 and th<strong>at</strong><br />
5<br />
passes through the point (3,−6)?<br />
1) y = 5<br />
x − 11<br />
3<br />
2) y = − 5<br />
x + 11<br />
3<br />
3) y = − 5<br />
x − 1<br />
3<br />
4) y = 5<br />
x + 1<br />
3<br />
103 Point A lies in plane B. How many lines can be<br />
drawn perpendicular to plane B through point A?<br />
1) one<br />
2) two<br />
3) zero<br />
4) infinite
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104 In the diagram below, PA and PB are tangent to<br />
circle O, OA and OB are radii, and OP intersects<br />
the circle <strong>at</strong> C. Prove: ∠AOP ≅ ∠BOP<br />
105 The coordin<strong>at</strong>es of the vertices of ABC are<br />
A(1,2), B(−4,3), and C(−3,−5). St<strong>at</strong>e the<br />
coordin<strong>at</strong>es of A' B' C', the image of ABC after<br />
a rot<strong>at</strong>ion of 90º about the origin. [The use of the<br />
set of axes below is optional.]<br />
106 In the diagram below, A′B′C ′ is a transform<strong>at</strong>ion<br />
of ABC, and A″B″C ″ is a transform<strong>at</strong>ion of<br />
A′B′C ′.<br />
The composite transform<strong>at</strong>ion of ABC to<br />
A″B″C ″ is an example of a<br />
1) reflection followed by a rot<strong>at</strong>ion<br />
2) reflection followed by a transl<strong>at</strong>ion<br />
3) transl<strong>at</strong>ion followed by a rot<strong>at</strong>ion<br />
4) transl<strong>at</strong>ion followed by a reflection<br />
107 Wh<strong>at</strong> is the length of AB with endpoints A(−1,0)<br />
and B(4,−3)?<br />
1) 6<br />
2) 18<br />
3) 34<br />
4) 50
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108 On the set of axes below, graph the locus of points<br />
th<strong>at</strong> are four units from the point (2,1). On the<br />
same set of axes, graph the locus of points th<strong>at</strong> are<br />
two units from the line x = 4. St<strong>at</strong>e the coordin<strong>at</strong>es<br />
of all points th<strong>at</strong> s<strong>at</strong>isfy both conditions.<br />
109 Wh<strong>at</strong> is the slope of a line perpendicular to the line<br />
whose equ<strong>at</strong>ion is 20x − 2y = 6?<br />
1) −10<br />
2) − 1<br />
10<br />
3) 10<br />
4)<br />
1<br />
10<br />
110 The equ<strong>at</strong>ion of line k is y = 1<br />
x − 2. The equ<strong>at</strong>ion<br />
3<br />
of line m is −2x + 6y = 18. Lines k and m are<br />
1) parallel<br />
2) perpendicular<br />
3) the same line<br />
4) neither parallel nor perpendicular<br />
111 Point P lies on line m. Point P is also included in<br />
distinct planes Q, R, S, and T. At most, how many<br />
of these planes could be perpendicular to line m?<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 4<br />
112 The slope of line is − 1<br />
. Wh<strong>at</strong> is an equ<strong>at</strong>ion of a<br />
3<br />
line th<strong>at</strong> is perpendicular to line ?<br />
1) y + 2 = 1<br />
3 x<br />
2) −2x + 6 = 6y<br />
3) 9x − 3y = 27<br />
4) 3x + y = 0<br />
113 Wh<strong>at</strong> is the slope of a line th<strong>at</strong> is perpendicular to<br />
the line whose equ<strong>at</strong>ion is 3x + 5y = 4?<br />
1) − 3<br />
5<br />
2)<br />
3<br />
5<br />
3) − 5<br />
4)<br />
5<br />
3<br />
3
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114 The coordin<strong>at</strong>es of the vertices of RST are<br />
R(−2,3), S(4,4), and T(2,−2). Triangle R′S ′T ′ is<br />
the image of RST after a rot<strong>at</strong>ion of 90° about<br />
the origin. St<strong>at</strong>e the coordin<strong>at</strong>es of the vertices of<br />
R′S ′T ′. [The use of the set of axes below is<br />
optional.]<br />
115 In circle O, diameter RS has endpoints<br />
R(3a,2b − 1) and S(a − 6,4b + 5). Find the<br />
coordin<strong>at</strong>es of point O, in terms of a and b.<br />
Express your answer in simplest form.<br />
116 Determine whether the two lines represented by the<br />
equ<strong>at</strong>ions y = 2x + 3 and 2y + x = 6 are parallel,<br />
perpendicular, or neither. Justify your response.<br />
117 As shown in the diagram below, FJ is contained in<br />
plane R, BC and DE are contained in plane S, and<br />
FJ , BC , and DE intersect <strong>at</strong> A.<br />
Which fact is not sufficient to show th<strong>at</strong> planes R<br />
and S are perpendicular?<br />
1) FA ⊥ DE<br />
2) AD ⊥ AF<br />
3) BC ⊥ FJ<br />
4) DE ⊥ BC<br />
118 In the diagram below of ABC, BC is extended to<br />
D.<br />
If m∠A = x 2 − 6x, m∠B = 2x − 3, and<br />
m∠ACD = 9x + 27, wh<strong>at</strong> is the value of x?<br />
1) 10<br />
2) 2<br />
3) 3<br />
4) 15
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119 Triangle HKL has vertices H(−7,2), K(3,−4), and<br />
L(5,4). The midpoint of HL is M and the midpoint<br />
of LK is N. Determine and st<strong>at</strong>e the coordin<strong>at</strong>es of<br />
points M and N. Justify the st<strong>at</strong>ement: MN is<br />
parallel to HK. [The use of the set of axes below is<br />
optional.]<br />
120 Which quadril<strong>at</strong>eral has diagonals th<strong>at</strong> always<br />
bisect its angles and also bisect each other?<br />
1) rhombus<br />
2) rectangle<br />
3) parallelogram<br />
4) isosceles trapezoid<br />
121 In the diagram below of ACE, medians AD, EB,<br />
and CF intersect <strong>at</strong> G. The length of FG is 12 cm.<br />
Wh<strong>at</strong> is the length, in centimeters, of GC?<br />
1) 24<br />
2) 12<br />
3) 6<br />
4) 4<br />
122 Wh<strong>at</strong> is an equ<strong>at</strong>ion of circle O shown in the graph<br />
below?<br />
1) (x + 1) 2 + (y − 3) 2 = 25<br />
2) (x − 1) 2 + (y + 3) 2 = 25<br />
3) (x − 5) 2 + (y + 6) 2 = 25<br />
4) (x + 5) 2 + (y − 6) 2 = 25
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123 Write an equ<strong>at</strong>ion of the circle graphed in the<br />
diagram below.<br />
124 Which set of numbers does not represent the sides<br />
of a right triangle?<br />
1) {6,8,10}<br />
2) {8,15,17}<br />
3) {8,24,25}<br />
4) {15,36,39}<br />
125 The equ<strong>at</strong>ion of a circle with its center <strong>at</strong> (−3,5)<br />
and a radius of 4 is<br />
1) (x + 3) 2 + (y − 5) 2 = 4<br />
2) (x − 3) 2 + (y + 5) 2 = 4<br />
3) (x + 3) 2 + (y − 5) 2 = 16<br />
4) (x − 3) 2 + (y + 5) 2 = 16<br />
126 When a dil<strong>at</strong>ion is performed on a hexagon, which<br />
property of the hexagon will not be preserved in its<br />
image?<br />
1) parallelism<br />
2) orient<strong>at</strong>ion<br />
3) length of sides<br />
4) measure of angles<br />
127 When solved graphically, wh<strong>at</strong> is the solution to<br />
the following system of equ<strong>at</strong>ions?<br />
y = x 2 − 4x + 6<br />
1) (1,4)<br />
2) (4,6)<br />
3) (1,3) and (4,6)<br />
4) (3,1) and (6,4)<br />
y = x + 2<br />
128 As shown on the set of axes below, GHS has<br />
vertices G(3,1), H(5,3), and S(1,4). Graph and<br />
st<strong>at</strong>e the coordin<strong>at</strong>es of G″H ″S ″, the image of<br />
GHS after the transform<strong>at</strong>ion T −3,1 D 2 .
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129 The diagram below shows the construction of AB → ←⎯<br />
through point P parallel to CD → ←⎯⎯<br />
.<br />
Which theorem justifies this method of<br />
construction?<br />
1) If two lines in a plane are perpendicular to a<br />
transversal <strong>at</strong> different points, then the lines are<br />
parallel.<br />
2) If two lines in a plane are cut by a transversal<br />
to form congruent corresponding angles, then<br />
the lines are parallel.<br />
3) If two lines in a plane are cut by a transversal<br />
to form congruent altern<strong>at</strong>e interior angles,<br />
then the lines are parallel.<br />
4) If two lines in a plane are cut by a transversal<br />
to form congruent altern<strong>at</strong>e exterior angles,<br />
then the lines are parallel.<br />
130 Parallelogram ABCD has coordin<strong>at</strong>es A(1,5),<br />
B(6,3), C(3,−1), and D(−2,1). Wh<strong>at</strong> are the<br />
coordin<strong>at</strong>es of E, the intersection of diagonals AC<br />
and BD?<br />
1) (2,2)<br />
2) (4.5,1)<br />
3) (3.5,2)<br />
4) (−1,3)<br />
131 A line segment has endpoints (4,7) and (1,11).<br />
Wh<strong>at</strong> is the length of the segment?<br />
1) 5<br />
2) 7<br />
3) 16<br />
4) 25<br />
132 Wh<strong>at</strong> are the center and the radius of the circle<br />
whose equ<strong>at</strong>ion is (x − 5) 2 + (y + 3) 2 = 16?<br />
1) (−5,3) and 16<br />
2) (5,−3) and 16<br />
3) (−5,3) and 4<br />
4) (5,−3) and 4<br />
133 In the diagram below, MATH is a rhombus with<br />
diagonals AH and MT.<br />
If m∠HAM = 12, wh<strong>at</strong> is m∠AMT ?<br />
1) 12<br />
2) 78<br />
3) 84<br />
4) 156
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134 In ABC, AB = 5 feet and BC = 3 feet. Which<br />
inequality represents all possible values for the<br />
length of AC, in feet?<br />
1) 2 ≤ AC ≤ 8<br />
2) 2 < AC < 8<br />
3) 3 ≤ AC ≤ 7<br />
4) 3 < AC < 7<br />
135 As shown in the diagram below, lines m and n are<br />
cut by transversal p.<br />
If m∠1 = 4x + 14 and m∠2 = 8x + 10, lines m and n<br />
are parallel when x equals<br />
1) 1<br />
2) 6<br />
3) 13<br />
4) 17<br />
136 Scalene triangle ABC is similar to triangle DEF.<br />
Which st<strong>at</strong>ement is false?<br />
1) AB :BC =DE:EF<br />
2) AC :DF =BC :EF<br />
3) ∠ACB ≅ ∠DFE<br />
4) ∠ABC ≅ ∠EDF<br />
137 The diagonals of a quadril<strong>at</strong>eral are congruent but<br />
do not bisect each other. This quadril<strong>at</strong>eral is<br />
1) an isosceles trapezoid<br />
2) a parallelogram<br />
3) a rectangle<br />
4) a rhombus<br />
138 Triangle ABC has coordin<strong>at</strong>es A(2,−2), B(2,1), and<br />
C(4,−2). Triangle A′B′C ′ is the image of ABC<br />
under T 5,−2 . On the set of axes below, graph and<br />
label ABC and its image, A′B′C ′. Determine<br />
the rel<strong>at</strong>ionship between the area of ABC and the<br />
area of A′B′C ′. Justify your response.<br />
139 The angle formed by the radius of a circle and a<br />
tangent to th<strong>at</strong> circle has a measure of<br />
1) 45°<br />
2) 90°<br />
3) 135°<br />
4) 180°
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140 Wh<strong>at</strong> is the equ<strong>at</strong>ion of a circle whose center is 4<br />
units above the origin in the coordin<strong>at</strong>e plane and<br />
whose radius is 6?<br />
1) x 2 + (y − 6) 2 = 16<br />
2) (x − 6) 2 + y 2 = 16<br />
3) x 2 + (y − 4) 2 = 36<br />
4) (x − 4) 2 + y 2 = 36<br />
141 A packing carton in the shape of a triangular prism<br />
is shown in the diagram below.<br />
Wh<strong>at</strong> is the volume, in cubic inches, of this carton?<br />
1) 20<br />
2) 60<br />
3) 120<br />
4) 240<br />
142 Which compound st<strong>at</strong>ement is true?<br />
1) A triangle has three sides and a quadril<strong>at</strong>eral<br />
has five sides.<br />
2) A triangle has three sides if and only if a<br />
quadril<strong>at</strong>eral has five sides.<br />
3) If a triangle has three sides, then a quadril<strong>at</strong>eral<br />
has five sides.<br />
4) A triangle has three sides or a quadril<strong>at</strong>eral has<br />
five sides.<br />
143 In the diagram below of circle O, diameter AB is<br />
perpendicular to chord CD <strong>at</strong> E. If AO = 10 and<br />
BE = 4, find the length of CE.<br />
144 Wh<strong>at</strong> is an equ<strong>at</strong>ion of the circle shown in the<br />
graph below?<br />
1) (x − 3) 2 + (y − 4) 2 = 25<br />
2) (x + 3) 2 + (y + 4) 2 = 25<br />
3) (x − 3) 2 + (y − 4) 2 = 10<br />
4) (x + 3) 2 + (y + 4) 2 = 10
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145 How many points are both 4 units from the origin<br />
and also 2 units from the line y = 4?<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 4<br />
146 The diameter of a sphere is 15 inches. Wh<strong>at</strong> is the<br />
volume of the sphere, to the nearest tenth of a<br />
cubic inch?<br />
1) 706.9<br />
2) 1767.1<br />
3) 2827.4<br />
4) 14,137.2<br />
147 In ABC shown below, P is the centroid and<br />
BF = 18.<br />
Wh<strong>at</strong> is the length of BP ?<br />
1) 6<br />
2) 9<br />
3) 3<br />
4) 12<br />
148 As shown in the diagram below, ABC ∼ DEF,<br />
AB = 7x, BC = 4, DE = 7, and EF = x.<br />
Wh<strong>at</strong> is the length of AB?<br />
1) 28<br />
2) 2<br />
3) 14<br />
4) 4<br />
149 When writing a geometric proof, which angle<br />
rel<strong>at</strong>ionship could be used alone to justify th<strong>at</strong> two<br />
angles are congruent?<br />
1) supplementary angles<br />
2) linear pair of angles<br />
3) adjacent angles<br />
4) vertical angles<br />
150 Find the slope of a line perpendicular to the line<br />
whose equ<strong>at</strong>ion is 2y − 6x = 4.<br />
151 Wh<strong>at</strong> is the volume, in cubic centimeters, of a<br />
cylinder th<strong>at</strong> has a height of 15 cm and a diameter<br />
of 12 cm?<br />
1) 180π<br />
2) 540π<br />
3) 675π<br />
4) 2,160π
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152 As shown in the diagram below, a kite needs a<br />
vertical and a horizontal support bar <strong>at</strong>tached <strong>at</strong><br />
opposite corners. The upper edges of the kite are 7<br />
inches, the side edges are x inches, and the vertical<br />
support bar is (x + 1) inches.<br />
Wh<strong>at</strong> is the measure, in inches, of the vertical<br />
support bar?<br />
1) 23<br />
2) 24<br />
3) 25<br />
4) 26<br />
153 Quadril<strong>at</strong>eral MNOP is a trapezoid with MN OP.<br />
If M ′N ′O′P ′ is the image of MNOP after a<br />
reflection over the x-axis, which two sides of<br />
quadril<strong>at</strong>eral M ′N ′O′P ′ are parallel?<br />
1) M ′N ′ and O′P ′<br />
2) M ′N ′ and N ′O′<br />
3) P ′M ′ and O′P ′<br />
4) P ′M ′ and N ′O′<br />
154 If AB → ←⎯<br />
is contained in plane P, and AB → ←⎯<br />
is<br />
perpendicular to plane R, which st<strong>at</strong>ement is true?<br />
1) AB → ←⎯<br />
is parallel to plane R.<br />
2) Plane P is parallel to plane R.<br />
3) AB → ←⎯<br />
is perpendicular to plane P.<br />
4) Plane P is perpendicular to plane R.<br />
155 The volume, in cubic centimeters, of a sphere<br />
whose diameter is 6 centimeters is<br />
1) 12π<br />
2) 36π<br />
3) 48π<br />
4) 288π<br />
156 In AED with ABCD shown in the diagram<br />
below, EB and EC are drawn.<br />
If AB ≅ CD, which st<strong>at</strong>ement could always be<br />
proven?<br />
1) AC ≅ DB<br />
2) AE ≅ ED<br />
3) AB ≅ BC<br />
4) EC ≅ EA
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157 Triangle TAP has coordin<strong>at</strong>es T(−1,4), A(2,4), and<br />
P(2,0). On the set of axes below, graph and label<br />
T ′A′P ′, the image of TAP after the transl<strong>at</strong>ion<br />
(x,y) → (x − 5,y − 1).<br />
158 In parallelogram ABCD shown below, diagonals<br />
AC and BD intersect <strong>at</strong> E.<br />
Which st<strong>at</strong>ement must be true?<br />
1) AC ≅ DB<br />
2) ∠ABD ≅ ∠CBD<br />
3) AED ≅ CEB<br />
4) DCE ≅ BCE<br />
159 The diagram below shows ABC, with AEB,<br />
ADC, and ∠ACB ≅ ∠AED. Prove th<strong>at</strong> ABC is<br />
similar to ADE.<br />
160 Which reason could be used to prove th<strong>at</strong> a<br />
parallelogram is a rhombus?<br />
1) Diagonals are congruent.<br />
2) Opposite sides are parallel.<br />
3) Diagonals are perpendicular.<br />
4) Opposite angles are congruent.<br />
161 In the diagram of ABC shown below, DE BC .<br />
If AB = 10, AD = 8, and AE = 12, wh<strong>at</strong> is the<br />
length of EC ?<br />
1) 6<br />
2) 2<br />
3) 3<br />
4) 15
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162 In the diagram below of circle O, chord AB is<br />
parallel to chord CD.<br />
Which st<strong>at</strong>ement must be true?<br />
1) AC ≅ BD<br />
2) AB ≅ CD<br />
3) AB ≅ CD<br />
4) ABD ≅ CDB<br />
163 In the diagram below, DE joins the midpoints of<br />
two sides of ABC.<br />
Which st<strong>at</strong>ement is not true?<br />
1) CE = 1<br />
2 CB<br />
2) DE = 1<br />
2 AB<br />
3) area of CDE = 1<br />
area of<br />
2<br />
CAB<br />
4) perimeter of CDE = 1<br />
perimeter of<br />
2<br />
CAB<br />
164 As shown in the diagram below, the diagonals of<br />
parallelogram QRST intersect <strong>at</strong> E. If<br />
QE = x 2 + 6x, SE = x + 14, and TE = 6x − 1,<br />
determine TE algebraically.<br />
165 In the diagram below of isosceles trapezoid ABCD,<br />
AB = CD = 25, AD = 26, and BC = 12.<br />
Wh<strong>at</strong> is the length of an altitude of the trapezoid?<br />
1) 7<br />
2) 14<br />
3) 19<br />
4) 24<br />
166 Plane R is perpendicular to line k and plane D is<br />
perpendicular to line k. Which st<strong>at</strong>ement is<br />
correct?<br />
1) Plane R is perpendicular to plane D.<br />
2) Plane R is parallel to plane D.<br />
3) Plane R intersects plane D.<br />
4) Plane R bisects plane D.
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167 Given: ABC with vertices A(−6,−2), B(2,8), and<br />
C(6,−2). AB has midpoint D, BC has midpoint E,<br />
and AC has midpoint F.<br />
Prove: ADEF is a parallelogram<br />
ADEF is not a rhombus<br />
[The use of the grid is optional.]<br />
168 A circle has the equ<strong>at</strong>ion (x − 2) 2 + (y + 3) 2 = 36.<br />
Wh<strong>at</strong> are the coordin<strong>at</strong>es of its center and the<br />
length of its radius?<br />
1) (−2,3) and 6<br />
2) (2,−3) and 6<br />
3) (−2,3) and 36<br />
4) (2,−3) and 36<br />
169 Triangle PQR has angles in the r<strong>at</strong>io of 2:3:5.<br />
Which type of triangle is PQR?<br />
1) acute<br />
2) isosceles<br />
3) obtuse<br />
4) right<br />
170 In the diagram of KLM below, m∠L = 70,<br />
m∠M = 50, and MK is extended through N.<br />
Wh<strong>at</strong> is the measure of ∠LKN ?<br />
1) 60º<br />
2) 120º<br />
3) 180º<br />
4) 300º<br />
171 The diagram below shows a pair of congruent<br />
triangles, with ∠ADB ≅ ∠CDB and<br />
∠ABD ≅ ∠CBD.<br />
Which st<strong>at</strong>ement must be true?<br />
1) ∠ADB ≅ ∠CBD<br />
2) ∠ABC ≅ ∠ADC<br />
3) AB ≅ CD<br />
4) AD ≅ CD
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172 The graph below shows JT and its image, J ′T ′,<br />
after a transform<strong>at</strong>ion.<br />
Which transform<strong>at</strong>ion would map JT onto J ′T ′?<br />
1) transl<strong>at</strong>ion<br />
2) glide reflection<br />
3) rot<strong>at</strong>ion centered <strong>at</strong> the origin<br />
4) reflection through the origin<br />
173 In circle O shown below, diameter DB is<br />
perpendicular to chord AC <strong>at</strong> E.<br />
If DB = 34, AC = 30, and DE > BE, wh<strong>at</strong> is the<br />
length of BE?<br />
1) 8<br />
2) 9<br />
3) 16<br />
4) 25<br />
174 In PQR, ∠PRQ is a right angle and RT is drawn<br />
perpendicular to hypotenuse PQ. If PT = x,<br />
RT = 6, and TQ = 4x, wh<strong>at</strong> is the length of PQ?<br />
1) 9<br />
2) 12<br />
3) 3<br />
4) 15<br />
175 In the diagram below, tangent ML and secant MNK<br />
are drawn to circle O. The r<strong>at</strong>io<br />
mLN : mNK : mKL is 3:4:5. Find m∠LMK .<br />
176 Wh<strong>at</strong> is the length of the line segment whose<br />
endpoints are A(−1,9) and B(7,4)?<br />
1) 61<br />
2) 89<br />
3) 205<br />
4) 233
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177 Which type of triangle can be drawn using the<br />
points (−2,3), (−2,−7), and (4,−5)?<br />
1) scalene<br />
2) isosceles<br />
3) equil<strong>at</strong>eral<br />
4) no triangle can be drawn<br />
178 The diagram below represents a rectangular solid.<br />
Which st<strong>at</strong>ement must be true?<br />
1) EH and BC are coplanar<br />
2) FG and AB are coplanar<br />
3) EH and AD are skew<br />
4) FG and CG are skew<br />
179 In the diagram below, two parallel lines intersect<br />
circle O <strong>at</strong> points A, B, C, and D, with<br />
mAB = x + 20 and mDC = 2x − 20. Find mAB.<br />
180 In the diagram below, point P is the centroid of<br />
ABC.<br />
If PM = 2x + 5 and BP = 7x + 4, wh<strong>at</strong> is the length<br />
of PM ?<br />
1) 9<br />
2) 2<br />
3) 18<br />
4) 27<br />
181 In the diagram below, EF is the median of<br />
trapezoid ABCD.<br />
If AB = 5x − 9, DC = x + 3, and EF = 2x + 2, wh<strong>at</strong><br />
is the value of x?<br />
1) 5<br />
2) 2<br />
3) 7<br />
4) 8
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182 Given: AD bisects BC <strong>at</strong> E.<br />
AB⊥ BC<br />
DC ⊥ BC<br />
Prove: AB ≅ DC<br />
183 In the diagram of ABC shown below, D is the<br />
midpoint of AB, E is the midpoint of BC , and F is<br />
the midpoint of AC.<br />
If AB = 20, BC = 12, and AC = 16, wh<strong>at</strong> is the<br />
perimeter of trapezoid ABEF?<br />
1) 24<br />
2) 36<br />
3) 40<br />
4) 44<br />
184 On the set of axes below, graph the locus of points<br />
th<strong>at</strong> are 4 units from the line x = 3 and the locus of<br />
points th<strong>at</strong> are 5 units from the point (0,2). Label<br />
with an X all points th<strong>at</strong> s<strong>at</strong>isfy both conditions.<br />
185 As shown in the diagram of ACD below, B is a<br />
point on AC and DB is drawn.<br />
If m∠A = 66, m∠CDB = 18, and m∠C = 24, wh<strong>at</strong><br />
is the longest side of ABD?<br />
1) AB<br />
2) DC<br />
3) AD<br />
4) BD
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186 In the diagram below of ABC, AB ≅ AC,<br />
m∠A = 3x, and m∠B = x + 20.<br />
Wh<strong>at</strong> is the value of x?<br />
1) 10<br />
2) 28<br />
3) 32<br />
4) 40<br />
187 Lines m and n intersect <strong>at</strong> point A. Line k is<br />
perpendicular to both lines m and n <strong>at</strong> point A.<br />
Which st<strong>at</strong>ement must be true?<br />
1) Lines m, n, and k are in the same plane.<br />
2) Lines m and n are in two different planes.<br />
3) Lines m and n are perpendicular to each other.<br />
4) Line k is perpendicular to the plane containing<br />
lines m and n.<br />
188 Wh<strong>at</strong> is the length of the line segment whose<br />
endpoints are (1,−4) and (9,2)?<br />
1) 5<br />
2) 2 17<br />
3) 10<br />
4) 2 26<br />
189 Given the true st<strong>at</strong>ement, "The medians of a<br />
triangle are concurrent," write the neg<strong>at</strong>ion of the<br />
st<strong>at</strong>ement and give the truth value for the neg<strong>at</strong>ion.<br />
190 In the diagram below of rhombus ABCD,<br />
m∠C = 100.<br />
Wh<strong>at</strong> is m∠DBC ?<br />
1) 40<br />
2) 45<br />
3) 50<br />
4) 80<br />
191 Which equ<strong>at</strong>ion represents the line th<strong>at</strong> is<br />
perpendicular to 2y = x + 2 and passes through the<br />
point (4,3)?<br />
1) y = 1<br />
x − 5<br />
2<br />
2) y = 1<br />
x + 1<br />
2<br />
3) y = −2x + 11<br />
4) y = −2x − 5<br />
192 Two lines are represented by the equ<strong>at</strong>ions<br />
x + 2y = 4 and 4y − 2x = 12. Determine whether<br />
these lines are parallel, perpendicular, or neither.<br />
Justify your answer.
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193 An equ<strong>at</strong>ion of the line th<strong>at</strong> passes through (2,−1)<br />
and is parallel to the line 2y + 3x = 8 is<br />
1) y = 3<br />
x − 4<br />
2<br />
2) y = 3<br />
x + 4<br />
2<br />
3) y = − 3<br />
x − 2<br />
2<br />
4) y = − 3<br />
x + 2<br />
2<br />
194 In the diagram below of PAO, AP is tangent to<br />
circle O <strong>at</strong> point A, OB = 7, and BP = 18.<br />
Wh<strong>at</strong> is the length of AP?<br />
1) 10<br />
2) 12<br />
3) 17<br />
4) 24<br />
195 In rhombus ABCD, the diagonals AC and BD<br />
intersect <strong>at</strong> E. If AE = 5 and BE = 12, wh<strong>at</strong> is the<br />
length of AB?<br />
1) 7<br />
2) 10<br />
3) 13<br />
4) 17<br />
196 In the diagram below of circle O, chords AB and<br />
CD intersect <strong>at</strong> E.<br />
If m∠AEC = 34 and mAC = 50, wh<strong>at</strong> is mDB ?<br />
1) 16<br />
2) 18<br />
3) 68<br />
4) 118<br />
197 Which equ<strong>at</strong>ion of a circle will have a graph th<strong>at</strong><br />
lies entirely in the first quadrant?<br />
1) (x − 4) 2 + (y − 5) 2 = 9<br />
2) (x + 4) 2 + (y + 5) 2 = 9<br />
3) (x + 4) 2 + (y + 5) 2 = 25<br />
4) (x − 5) 2 + (y − 4) 2 = 25<br />
198 In RST, m∠R = 58 and m∠S = 73. Which<br />
inequality is true?<br />
1) RT < TS < RS<br />
2) RS < RT < TS<br />
3) RT < RS < TS<br />
4) RS < TS < RT
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199 Line n intersects lines l and m, forming the angles<br />
shown in the diagram below.<br />
Which value of x would prove l m?<br />
1) 2.5<br />
2) 4.5<br />
3) 6.25<br />
4) 8.75<br />
200 The vertices of RST are R(−6,5), S(−7,−2), and<br />
T(1,4). The image of RST after the composition<br />
T−2,3 r y = x is R"S"T". St<strong>at</strong>e the coordin<strong>at</strong>es of<br />
R"S"T". [The use of the set of axes below is<br />
optional.]<br />
201 Quadril<strong>at</strong>eral MATH has coordin<strong>at</strong>es M(1,1),<br />
A(−2,5), T(3,5), and H(6,1). Prove th<strong>at</strong><br />
quadril<strong>at</strong>eral MATH is a rhombus and prove th<strong>at</strong> it<br />
is not a square. [The use of the grid is optional.]<br />
202 In the diagram below of circle O, PA is tangent to<br />
circle O <strong>at</strong> A, and PBC is a secant with points B<br />
and C on the circle.<br />
If PA = 8 and PB = 4, wh<strong>at</strong> is the length of BC ?<br />
1) 20<br />
2) 16<br />
3) 15<br />
4) 12
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203 In the diagram below of right triangle ABC, altitude<br />
BD is drawn to hypotenuse AC, AC = 16, and<br />
CD = 7.<br />
Wh<strong>at</strong> is the length of BD?<br />
1) 3 7<br />
2) 4 7<br />
3) 7 3<br />
4) 12<br />
204 Triangle ABC is graphed on the set of axes below.<br />
Which transform<strong>at</strong>ion produces an image th<strong>at</strong> is<br />
similar to, but not congruent to, ABC?<br />
1) T2,3 2) D 2<br />
3) r y = x<br />
4) R 90<br />
205 In the diagram below of circle O, chord AB bisects<br />
chord CD <strong>at</strong> E. If AE = 8 and BE = 9, find the<br />
length of CE in simplest radical form.<br />
206 Wh<strong>at</strong> is an equ<strong>at</strong>ion of circle O shown in the graph<br />
below?<br />
1) (x + 2) 2 + (y − 2) 2 = 9<br />
2) (x + 2) 2 + (y − 2) 2 = 3<br />
3) (x − 2) 2 + (y + 2) 2 = 9<br />
4) (x − 2) 2 + (y + 2) 2 = 3
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207 In the diagram below, ABC is circumscribed<br />
about circle O and the sides of ABC are tangent<br />
to the circle <strong>at</strong> points D, E, and F.<br />
If AB = 20, AE = 12, and CF = 15, wh<strong>at</strong> is the<br />
length of AC?<br />
1) 8<br />
2) 15<br />
3) 23<br />
4) 27<br />
208 In the diagram of JEA below, m∠JEA = 90 and<br />
m∠EAJ = 48. Line segment MS connects points M<br />
and S on the triangle, such th<strong>at</strong> m∠EMS = 59.<br />
Wh<strong>at</strong> is m∠JSM ?<br />
1) 163<br />
2) 121<br />
3) 42<br />
4) 17<br />
209 Wh<strong>at</strong> is an equ<strong>at</strong>ion of a circle with center (7,−3)<br />
and radius 4?<br />
1) (x − 7) 2 + (y + 3) 2 = 4<br />
2) (x + 7) 2 + (y − 3) 2 = 4<br />
3) (x − 7) 2 + (y + 3) 2 = 16<br />
4) (x + 7) 2 + (y − 3) 2 = 16<br />
210 In the diagram below of DAE and BCE, AB<br />
and CD intersect <strong>at</strong> E, such th<strong>at</strong> AE ≅ CE and<br />
∠BCE ≅ ∠DAE.<br />
Triangle DAE can be proved congruent to triangle<br />
BCE by<br />
1) ASA<br />
2) SAS<br />
3) SSS<br />
4) HL<br />
211 If the vertex angles of two isosceles triangles are<br />
congruent, then the triangles must be<br />
1) acute<br />
2) congruent<br />
3) right<br />
4) similar
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212 In the diagram below of ABC, TV → ←⎯<br />
BC , AT = 5,<br />
TB = 7, and AV = 10.<br />
Wh<strong>at</strong> is the length of VC?<br />
1) 3 1<br />
2<br />
2) 7 1<br />
7<br />
3) 14<br />
4) 24<br />
213 The two lines represented by the equ<strong>at</strong>ions below<br />
are graphed on a coordin<strong>at</strong>e plane.<br />
x + 6y = 12<br />
3(x − 2) = −y − 4<br />
Which st<strong>at</strong>ement best describes the two lines?<br />
1) The lines are parallel.<br />
2) The lines are the same line.<br />
3) The lines are perpendicular.<br />
4) The lines intersect <strong>at</strong> an angle other than 90°.<br />
214 Wh<strong>at</strong> is an equ<strong>at</strong>ion of the circle with a radius of 5<br />
and center <strong>at</strong> (1,−4)?<br />
1) (x + 1) 2 + (y − 4) 2 = 5<br />
2) (x − 1) 2 + (y + 4) 2 = 5<br />
3) (x + 1) 2 + (y − 4) 2 = 25<br />
4) (x − 1) 2 + (y + 4) 2 = 25<br />
215 On the set of axes below, solve the system of<br />
equ<strong>at</strong>ions graphically and st<strong>at</strong>e the coordin<strong>at</strong>es of<br />
all points in the solution.<br />
y = (x − 2) 2 − 3<br />
2y + 16 = 4x<br />
216 In the diagram below, AB, BC , and AC are<br />
tangents to circle O <strong>at</strong> points F, E, and D,<br />
respectively, AF = 6, CD = 5, and BE = 4.<br />
Wh<strong>at</strong> is the perimeter of ABC?<br />
1) 15<br />
2) 25<br />
3) 30<br />
4) 60
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217 The vertices of the triangle in the diagram below<br />
are A(7,9), B(3,3), and C(11,3).<br />
Wh<strong>at</strong> are the coordin<strong>at</strong>es of the centroid of<br />
ABC?<br />
1) (5,6)<br />
2) (7,3)<br />
3) (7,5)<br />
4) (9,6)<br />
218 In the diagram below, lines n and m are cut by<br />
transversals p and q.<br />
Wh<strong>at</strong> value of x would make lines n and m parallel?<br />
1) 110<br />
2) 80<br />
3) 70<br />
4) 50<br />
219 On the set of axes below, solve the following<br />
system of equ<strong>at</strong>ions graphically and st<strong>at</strong>e the<br />
coordin<strong>at</strong>es of all points in the solution.<br />
(x + 3) 2 + (y − 2) 2 = 25<br />
2y + 4 = −x<br />
220 Triangle ABC has vertices A(0,0), B(3,2), and<br />
C(0,4). The triangle may be classified as<br />
1) equil<strong>at</strong>eral<br />
2) isosceles<br />
3) right<br />
4) scalene<br />
221 A sphere is inscribed inside a cube with edges of 6<br />
cm. In cubic centimeters, wh<strong>at</strong> is the volume of the<br />
sphere, in terms of π?<br />
1) 12π<br />
2) 36π<br />
3) 48π<br />
4) 288π
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222 The number of degrees in the sum of the interior<br />
angles of a pentagon is<br />
1) 72<br />
2) 360<br />
3) 540<br />
4) 720<br />
223 The graph below shows the locus of points<br />
equidistant from the x-axis and y-axis. On the same<br />
set of axes, graph the locus of points 3 units from<br />
the line x = 0. Label with an X all points th<strong>at</strong><br />
s<strong>at</strong>isfy both conditions.<br />
224 A cylinder has a height of 7 cm and a base with a<br />
diameter of 10 cm. Determine the volume, in cubic<br />
centimeters, of the cylinder in terms of π .<br />
225 When ABC is dil<strong>at</strong>ed by a scale factor of 2, its<br />
image is A′B′C ′. Which st<strong>at</strong>ement is true?<br />
1) AC ≅ A′C ′<br />
2) ∠A ≅ ∠A′<br />
3) perimeter of ABC = perimeter of A′B′C ′<br />
4) 2(area of ABC) = area of A′B′C ′<br />
226 In the diagram below of circle O, chords RT and<br />
QS intersect <strong>at</strong> M. Secant PTR and tangent PS are<br />
drawn to circle O. The length of RM is two more<br />
than the length of TM , QM = 2, SM = 12, and<br />
PT = 8.<br />
Find the length of RT . Find the length of PS .
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227 In the diagram below, circles X and Y have two<br />
tangents drawn to them from external point T. The<br />
points of tangency are C, A, S, and E. The r<strong>at</strong>io of<br />
TA to AC is 1:3. If TS = 24, find the length of SE.<br />
228 In ABC, m∠A = x, m∠B = 2x + 2, and<br />
m∠C = 3x + 4. Wh<strong>at</strong> is the value of x?<br />
1) 29<br />
2) 31<br />
3) 59<br />
4) 61<br />
229 Lines j and k intersect <strong>at</strong> point P. Line m is drawn<br />
so th<strong>at</strong> it is perpendicular to lines j and k <strong>at</strong> point P.<br />
Which st<strong>at</strong>ement is correct?<br />
1) Lines j and k are in perpendicular planes.<br />
2) Line m is in the same plane as lines j and k.<br />
3) Line m is parallel to the plane containing lines j<br />
and k.<br />
4) Line m is perpendicular to the plane containing<br />
lines j and k.<br />
230 In the diagram of ABC and EDC below, AE<br />
and BD intersect <strong>at</strong> C, and ∠CAB ≅ ∠CED.<br />
Which method can be used to show th<strong>at</strong> ABC<br />
must be similar to EDC?<br />
1) SAS<br />
2) AA<br />
3) SSS<br />
4) HL<br />
231 On the grid below, graph the points th<strong>at</strong> are<br />
equidistant from both the x and y axes and the<br />
points th<strong>at</strong> are 5 units from the origin. Label with<br />
an X all points th<strong>at</strong> s<strong>at</strong>isfy both conditions.
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232 Write a st<strong>at</strong>ement th<strong>at</strong> is logically equivalent to the<br />
st<strong>at</strong>ement “If two sides of a triangle are congruent,<br />
the angles opposite those sides are congruent.”<br />
Identify the new st<strong>at</strong>ement as the converse, inverse,<br />
or contrapositive of the original st<strong>at</strong>ement.<br />
233 Wh<strong>at</strong> is an equ<strong>at</strong>ion of the line th<strong>at</strong> passes through<br />
the point (−2,5) and is perpendicular to the line<br />
whose equ<strong>at</strong>ion is y = 1<br />
x + 5?<br />
1) y = 2x + 1<br />
2) y = −2x + 1<br />
3) y = 2x + 9<br />
4) y = −2x − 9<br />
234 The l<strong>at</strong>eral faces of a regular pyramid are<br />
composed of<br />
1) squares<br />
2) rectangles<br />
3) congruent right triangles<br />
4) congruent isosceles triangles<br />
235 Wh<strong>at</strong> is the equ<strong>at</strong>ion of a line th<strong>at</strong> passes through<br />
the point (−3,−11) and is parallel to the line whose<br />
equ<strong>at</strong>ion is 2x − y = 4?<br />
1) y = 2x + 5<br />
2) y = 2x − 5<br />
3) y = 1 25<br />
x +<br />
2 2<br />
4) y = − 1 25<br />
x −<br />
2 2<br />
236 In RST, m∠RST = 46 and RS ≅ ST. Find<br />
m∠STR.<br />
2<br />
237 In the diagram below, ABC ≅ XYZ.<br />
Which two st<strong>at</strong>ements identify corresponding<br />
congruent parts for these triangles?<br />
1) AB ≅ XY and ∠C ≅ ∠Y<br />
2) AB ≅ YZ and ∠C ≅ ∠X<br />
3) BC ≅ XY and ∠A ≅ ∠Y<br />
4) BC ≅ YZ and ∠A ≅ ∠X<br />
238 Find an equ<strong>at</strong>ion of the line passing through the<br />
point (5,4) and parallel to the line whose equ<strong>at</strong>ion<br />
is 2x + y = 3.<br />
239 In the diagram below of circle O, chords AE and<br />
DC intersect <strong>at</strong> point B, such th<strong>at</strong> mAC = 36 and<br />
mDE = 20.<br />
Wh<strong>at</strong> is m∠ABC ?<br />
1) 56<br />
2) 36<br />
3) 28<br />
4) 8
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240 In the diagram below, car A is parked 7 miles from<br />
car B. Sketch the points th<strong>at</strong> are 4 miles from car A<br />
and sketch the points th<strong>at</strong> are 4 miles from car B.<br />
Label with an X all points th<strong>at</strong> s<strong>at</strong>isfy both<br />
conditions.<br />
241 Wh<strong>at</strong> is an equ<strong>at</strong>ion of a circle with its center <strong>at</strong><br />
(−3,5) and a radius of 4?<br />
1) (x − 3) 2 + (y + 5) 2 = 16<br />
2) (x + 3) 2 + (y − 5) 2 = 16<br />
3) (x − 3) 2 + (y + 5) 2 = 4<br />
4) (x + 3) 2 + (y − 5) 2 = 4<br />
242 Wh<strong>at</strong> are the center and radius of a circle whose<br />
equ<strong>at</strong>ion is (x − A) 2 + (y − B) 2 = C?<br />
1) center = (A,B); radius = C<br />
2) center = (−A,−B); radius = C<br />
3) center = (A,B); radius = C<br />
4) center = (−A,−B); radius = C<br />
243 Wh<strong>at</strong> is the measure of an interior angle of a<br />
regular octagon?<br />
1) 45º<br />
2) 60º<br />
3) 120º<br />
4) 135º<br />
244 If a line segment has endpoints A(3x + 5,3y) and<br />
B(x − 1,−y), wh<strong>at</strong> are the coordin<strong>at</strong>es of the<br />
midpoint of AB?<br />
1) (x + 3,2y)<br />
2) (2x + 2,y)<br />
3) (2x + 3,y)<br />
4) (4x + 4,2y)<br />
245 The vertices of ABC are A(3,2), B(6,1), and<br />
C(4,6). Identify and graph a transform<strong>at</strong>ion of<br />
ABC such th<strong>at</strong> its image, A′B′C ′, results in<br />
AB A′B′.
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246 Given: ABC and EDC, C is the midpoint of<br />
BD and AE<br />
Prove: AB DE<br />
247 In the diagram below of AGE and OLD,<br />
∠GAE ≅ ∠LOD, and AE ≅ OD.<br />
To prove th<strong>at</strong> AGE and OLD are congruent by<br />
SAS, wh<strong>at</strong> other inform<strong>at</strong>ion is needed?<br />
1) GE ≅ LD<br />
2) AG ≅ OL<br />
3) ∠AGE ≅ ∠OLD<br />
4) ∠AEG ≅ ∠ODL<br />
248 Wh<strong>at</strong> is the solution of the following system of<br />
equ<strong>at</strong>ions?<br />
y = (x + 3) 2 − 4<br />
y = 2x + 5<br />
1) (0,−4)<br />
2) (−4,0)<br />
3) (−4,−3) and (0,5)<br />
4) (−3,−4) and (5,0)<br />
249 Which expression best describes the transform<strong>at</strong>ion<br />
shown in the diagram below?<br />
1) same orient<strong>at</strong>ion; reflection<br />
2) opposite orient<strong>at</strong>ion; reflection<br />
3) same orient<strong>at</strong>ion; transl<strong>at</strong>ion<br />
4) opposite orient<strong>at</strong>ion; transl<strong>at</strong>ion<br />
250 Which transform<strong>at</strong>ion can map the letter S onto<br />
itself?<br />
1) glide reflection<br />
2) transl<strong>at</strong>ion<br />
3) line reflection<br />
4) rot<strong>at</strong>ion<br />
251 In KLM , m∠K = 36 and KM = 5. The<br />
transform<strong>at</strong>ion D 2 is performed on KLM to form<br />
K ′L′M ′. Find m∠K ′. Justify your answer.<br />
Find the length of K ′M ′. Justify your answer.
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252 The coordin<strong>at</strong>es of the vertices of ABC A(1,3),<br />
B(−2,2) and C(0,−2). On the grid below, graph<br />
and label A″B″C ″, the result of the composite<br />
transform<strong>at</strong>ion D 2 T 3,−2 . St<strong>at</strong>e the coordin<strong>at</strong>es of<br />
A″, B″, and C ″.<br />
253 In the diagram below, which transform<strong>at</strong>ion was<br />
used to map ABC to A′B′C ′?<br />
1) dil<strong>at</strong>ion<br />
2) rot<strong>at</strong>ion<br />
3) reflection<br />
4) glide reflection<br />
254 Write an equ<strong>at</strong>ion of the perpendicular bisector of<br />
the line segment whose endpoints are (−1,1) and<br />
(7,−5). [The use of the grid below is optional]<br />
255 In the diagram below of ABC, DE is a<br />
midsegment of ABC, DE = 7, AB = 10, and<br />
BC = 13. Find the perimeter of ABC.<br />
256 In right DEF, m∠D = 90 and m∠F is 12 degrees<br />
less than twice m∠E . Find m∠E .
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257 Given: Two is an even integer or three is an even<br />
integer.<br />
Determine the truth value of this disjunction.<br />
Justify your answer.<br />
258 In the diagram below of circle C, mQT = 140, and<br />
m∠P = 40.<br />
Wh<strong>at</strong> is mRS ?<br />
1) 50<br />
2) 60<br />
3) 90<br />
4) 110<br />
259 Wh<strong>at</strong> is the slope of a line perpendicular to the line<br />
whose equ<strong>at</strong>ion is y = − 2<br />
x − 5?<br />
3<br />
1) − 3<br />
2<br />
2) − 2<br />
3<br />
3)<br />
2<br />
3<br />
4)<br />
3<br />
2<br />
260 On the set of axes below, graph and label DEF<br />
with vertices <strong>at</strong> D(−4,−4), E(−2,2), and F(8,−2). If<br />
G is the midpoint of EF and H is the midpoint of<br />
DF, st<strong>at</strong>e the coordin<strong>at</strong>es of G and H and label<br />
each point on your graph. Explain why GH DE.<br />
261 In the diagram below of right triangle ACB, altitude<br />
CD is drawn to hypotenuse AB.<br />
If AB = 36 and AC = 12, wh<strong>at</strong> is the length of AD?<br />
1) 32<br />
2) 6<br />
3) 3<br />
4) 4
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262 The diagram below shows the construction of the<br />
center of the circle circumscribed about ABC.<br />
This construction represents how to find the<br />
intersection of<br />
1) the angle bisectors of ABC<br />
2) the medians to the sides of ABC<br />
3) the altitudes to the sides of ABC<br />
4) the perpendicular bisectors of the sides of<br />
ABC<br />
263 In the diagram of circle O below, chords AB and<br />
CD are parallel, and BD is a diameter of the circle.<br />
If mAD = 60, wh<strong>at</strong> is m∠CDB?<br />
1) 20<br />
2) 30<br />
3) 60<br />
4) 120<br />
264 In the diagram below, circle O has a radius of 5,<br />
and CE = 2. Diameter AC is perpendicular to<br />
chord BD <strong>at</strong> E.<br />
Wh<strong>at</strong> is the length of BD?<br />
1) 12<br />
2) 10<br />
3) 8<br />
4) 4<br />
265 In the diagram below of circle O,<br />
chord AB chord CD, and chord CD chord EF .<br />
Which st<strong>at</strong>ement must be true?<br />
1) CE ≅ DF<br />
2) AC ≅ DF<br />
3) AC ≅ CE<br />
4) EF ≅ CD
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266 In a coordin<strong>at</strong>e plane, how many points are both 5<br />
units from the origin and 2 units from the x-axis?<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 4<br />
267 In the diagram below, line k is perpendicular to<br />
plane P <strong>at</strong> point T.<br />
Which st<strong>at</strong>ement is true?<br />
1) Any point in plane P also will be on line k.<br />
2) Only one line in plane P will intersect line k.<br />
3) All planes th<strong>at</strong> intersect plane P will pass<br />
through T.<br />
4) Any plane containing line k is perpendicular to<br />
plane P.<br />
268 Wh<strong>at</strong> is the inverse of the st<strong>at</strong>ement “If two<br />
triangles are not similar, their corresponding angles<br />
are not congruent”?<br />
1) If two triangles are similar, their corresponding<br />
angles are not congruent.<br />
2) If corresponding angles of two triangles are not<br />
congruent, the triangles are not similar.<br />
3) If two triangles are similar, their corresponding<br />
angles are congruent.<br />
4) If corresponding angles of two triangles are<br />
congruent, the triangles are similar.<br />
269 In the diagram below of ACT, D is the midpoint<br />
of AC, O is the midpoint of AT, and G is the<br />
midpoint of CT.<br />
If AC = 10, AT = 18, and CT = 22, wh<strong>at</strong> is the<br />
perimeter of parallelogram CDOG?<br />
1) 21<br />
2) 25<br />
3) 32<br />
4) 40<br />
270 Which geometric principle is used to justify the<br />
construction below?<br />
1) A line perpendicular to one of two parallel<br />
lines is perpendicular to the other.<br />
2) Two lines are perpendicular if they intersect to<br />
form congruent adjacent angles.<br />
3) When two lines are intersected by a transversal<br />
and altern<strong>at</strong>e interior angles are congruent, the<br />
lines are parallel.<br />
4) When two lines are intersected by a transversal<br />
and the corresponding angles are congruent, the<br />
lines are parallel.
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271 In the diagram below, RST is a 3 − 4 − 5 right<br />
triangle. The altitude, h, to the hypotenuse has<br />
been drawn. Determine the length of h.<br />
272 On the set of axes below, sketch the points th<strong>at</strong> are<br />
5 units from the origin and sketch the points th<strong>at</strong><br />
are 2 units from the line y = 3. Label with an X all<br />
points th<strong>at</strong> s<strong>at</strong>isfy both conditions.<br />
273 Using a compass and straightedge, and AB below,<br />
construct an equil<strong>at</strong>eral triangle with all sides<br />
congruent to AB. [Leave all construction marks.]<br />
274 A quadril<strong>at</strong>eral whose diagonals bisect each other<br />
and are perpendicular is a<br />
1) rhombus<br />
2) rectangle<br />
3) trapezoid<br />
4) parallelogram<br />
275 In the diagram below of circle O, chords AD and<br />
BC intersect <strong>at</strong> E, mAC = 87, and mBD = 35.<br />
Wh<strong>at</strong> is the degree measure of ∠CEA?<br />
1) 87<br />
2) 61<br />
3) 43.5<br />
4) 26
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276 Lines k 1 and k 2 intersect <strong>at</strong> point E. Line m is<br />
perpendicular to lines k 1 and k 2 <strong>at</strong> point E.<br />
Which st<strong>at</strong>ement is always true?<br />
1) Lines k 1 and k 2 are perpendicular.<br />
2) Line m is parallel to the plane determined by<br />
lines k 1 and k 2 .<br />
3) Line m is perpendicular to the plane<br />
determined by lines k 1 and k 2 .<br />
4) Line m is coplanar with lines k 1 and k 2 .<br />
277 In ABC, AB ≅ BC . An altitude is drawn from B<br />
to AC and intersects AC <strong>at</strong> D. Which conclusion is<br />
not always true?<br />
1) ∠ABD ≅ ∠CBD<br />
2) ∠BDA ≅ ∠BDC<br />
3) AD ≅ BD<br />
4) AD ≅ DC<br />
278 A right circular cylinder has a volume of 1,000<br />
cubic inches and a height of 8 inches. Wh<strong>at</strong> is the<br />
radius of the cylinder to the nearest tenth of an<br />
inch?<br />
1) 6.3<br />
2) 11.2<br />
3) 19.8<br />
4) 39.8<br />
279 The diagram below shows a right pentagonal prism.<br />
Which st<strong>at</strong>ement is always true?<br />
1) BC ED<br />
2) FG CD<br />
3) FJ IH<br />
4) GB HC
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280 The diagram below shows isosceles trapezoid<br />
ABCD with AB DC and AD ≅ BC . If<br />
m∠BAD = 2x and m∠BCD = 3x + 5, find m∠BAD.<br />
281 Triangle ABC has coordin<strong>at</strong>es A(−6,2), B(−3,6),<br />
and C(5,0). Find the perimeter of the triangle.<br />
Express your answer in simplest radical form. [The<br />
use of the grid below is optional.]<br />
282 Which st<strong>at</strong>ement is logically equivalent to "If it is<br />
warm, then I go swimming"<br />
1) If I go swimming, then it is warm.<br />
2) If it is warm, then I do not go swimming.<br />
3) If I do not go swimming, then it is not warm.<br />
4) If it is not warm, then I do not go swimming.<br />
283 In the diagram below of circle O, chords AD and<br />
BC intersect <strong>at</strong> E.<br />
Which rel<strong>at</strong>ionship must be true?<br />
1) CAE ≅ DBE<br />
2) AEC ∼ BED<br />
3) ∠ACB ≅ ∠CBD<br />
4) CA ≅ DB<br />
284 Given ABC with base AFEDC, median BF ,<br />
altitude BD, and BE bisects ∠ABC, which<br />
conclusion is valid?<br />
1) ∠FAB ≅ ∠ABF<br />
2) ∠ABF ≅ ∠CBD<br />
3) CE ≅ EA<br />
4) CF ≅ FA
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285 In the diagram below, quadril<strong>at</strong>eral STAR is a<br />
rhombus with diagonals SA and TR intersecting <strong>at</strong><br />
E. ST = 3x + 30, SR = 8x − 5, SE = 3z, TE = 5z + 5,<br />
AE = 4z − 8, m∠RTA = 5y − 2, and<br />
m∠TAS = 9y + 8. Find SR, RT, and m∠TAS .<br />
286 Based on the construction below, which st<strong>at</strong>ement<br />
must be true?<br />
1) m∠ABD = 1<br />
2 m∠CBD<br />
2) m∠ABD = m∠CBD<br />
3) m∠ABD = m∠ABC<br />
4) m∠CBD = 1<br />
2 m∠ABD<br />
287 Line k is drawn so th<strong>at</strong> it is perpendicular to two<br />
distinct planes, P and R. Wh<strong>at</strong> must be true about<br />
planes P and R?<br />
1) Planes P and R are skew.<br />
2) Planes P and R are parallel.<br />
3) Planes P and R are perpendicular.<br />
4) Plane P intersects plane R but is not<br />
perpendicular to plane R.<br />
288 Write an equ<strong>at</strong>ion of the line th<strong>at</strong> passes through<br />
the point (6,−5) and is parallel to the line whose<br />
equ<strong>at</strong>ion is 2x − 3y = 11.<br />
289 Tim has a rectangular prism with a length of 10<br />
centimeters, a width of 2 centimeters, and an<br />
unknown height. He needs to build another<br />
rectangular prism with a length of 5 centimeters<br />
and the same height as the original prism. The<br />
volume of the two prisms will be the same. Find<br />
the width, in centimeters, of the new prism.<br />
290 If two different lines are perpendicular to the same<br />
plane, they are<br />
1) collinear<br />
2) coplanar<br />
3) congruent<br />
4) consecutive
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291 Triangle XYZ, shown in the diagram below, is<br />
reflected over the line x = 2. St<strong>at</strong>e the coordin<strong>at</strong>es<br />
of X ′Y ′Z′, the image of XYZ.<br />
292 A right circular cone has a base with a radius of 15<br />
cm, a vertical height of 20 cm, and a slant height of<br />
25 cm. Find, in terms of' π , the number of square<br />
centimeters in the l<strong>at</strong>eral area of the cone.<br />
293 Given the system of equ<strong>at</strong>ions: y = x 2 − 4x<br />
x = 4<br />
The number of points of intersection is<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 0<br />
294 In the diagram below, quadril<strong>at</strong>eral ABCD is<br />
inscribed in circle O, AB DC , and diagonals AC<br />
and BD are drawn. Prove th<strong>at</strong> ACD ≅ BDC.<br />
295 Tim is going to paint a wooden sphere th<strong>at</strong> has a<br />
diameter of 12 inches. Find the surface area of the<br />
sphere, to the nearest square inch.<br />
296 Through a given point, P, on a plane, how many<br />
lines can be drawn th<strong>at</strong> are perpendicular to th<strong>at</strong><br />
plane?<br />
1) 1<br />
2) 2<br />
3) more than 2<br />
4) none
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297 In the diagram below of HQP, side HP is<br />
extended through P to T, m∠QPT = 6x + 20,<br />
m∠HQP = x + 40, and m∠PHQ = 4x − 5. Find<br />
m∠QPT .<br />
298 In the diagram below of quadril<strong>at</strong>eral ABCD with<br />
diagonal BD, m∠A = 93, m∠ADB = 43,<br />
m∠C = 3x + 5, m∠BDC = x + 19, and<br />
m∠DBC = 2x + 6. Determine if AB is parallel to<br />
DC . Explain your reasoning.<br />
299 In the diagram below of parallelogram STUV,<br />
SV = x + 3, VU = 2x − 1, and TU = 4x − 3.<br />
Wh<strong>at</strong> is the length of SV?<br />
1) 5<br />
2) 2<br />
3) 7<br />
4) 4<br />
300 In the diagram below, tangent PA and secant PBC<br />
are drawn to circle O from external point P.<br />
If PB = 4 and BC = 5, wh<strong>at</strong> is the length of PA?<br />
1) 20<br />
2) 9<br />
3) 8<br />
4) 6
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301 The coordin<strong>at</strong>es of the vertices of parallelogram<br />
ABCD are A(−2,2), B(3,5), C(4,2), and D(−1,−1).<br />
St<strong>at</strong>e the coordin<strong>at</strong>es of the vertices of<br />
parallelogram A″B″C ″D″ th<strong>at</strong> result from the<br />
transform<strong>at</strong>ion r y − axis T 2,−3 . [The use of the set of<br />
axes below is optional. ]<br />
302 Wh<strong>at</strong> are the center and the radius of the circle<br />
whose equ<strong>at</strong>ion is (x − 3) 2 + (y + 3) 2 = 36<br />
1) center = (3,−3); radius = 6<br />
2) center = (−3,3); radius = 6<br />
3) center = (3,−3); radius = 36<br />
4) center = (−3,3); radius = 36<br />
303 If ABC ∼ ZXY, m∠A = 50, and m∠C = 30,<br />
wh<strong>at</strong> is m∠X ?<br />
1) 30<br />
2) 50<br />
3) 80<br />
4) 100<br />
304 Two triangles are similar, and the r<strong>at</strong>io of each pair<br />
of corresponding sides is 2:1. Which st<strong>at</strong>ement<br />
regarding the two triangles is not true?<br />
1) Their areas have a r<strong>at</strong>io of 4:1.<br />
2) Their altitudes have a r<strong>at</strong>io of 2:1.<br />
3) Their perimeters have a r<strong>at</strong>io of 2:1.<br />
4) Their corresponding angles have a r<strong>at</strong>io of 2:1.<br />
305 The coordin<strong>at</strong>es of the vertices of parallelogram<br />
ABCD are A(−3,2), B(−2,−1), C(4,1), and D(3,4).<br />
The slopes of which line segments could be<br />
calcul<strong>at</strong>ed to show th<strong>at</strong> ABCD is a rectangle?<br />
1) AB and DC<br />
2) AB and BC<br />
3) AD and BC<br />
4) AC and BD<br />
306 In isosceles triangle ABC, AB = BC. Which<br />
st<strong>at</strong>ement will always be true?<br />
1) m∠B = m∠A<br />
2) m∠A > m∠B<br />
3) m∠A = m∠C<br />
4) m∠C < m∠B<br />
307 Line segment AB has endpoints A(2,−3) and<br />
B(−4,6). Wh<strong>at</strong> are the coordin<strong>at</strong>es of the midpoint<br />
of AB?<br />
1) (−2,3)<br />
2) −1,1 1 <br />
<br />
2 <br />
3) (−1,3)<br />
4) 3,4 1 <br />
<br />
2
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308 Which transform<strong>at</strong>ion is not always an isometry?<br />
1) rot<strong>at</strong>ion<br />
2) dil<strong>at</strong>ion<br />
3) reflection<br />
4) transl<strong>at</strong>ion<br />
309 On the set of axes below, Geoff drew rectangle<br />
ABCD. He will transform the rectangle by using<br />
the transl<strong>at</strong>ion (x,y) → (x + 2,y + 1) and then will<br />
reflect the transl<strong>at</strong>ed rectangle over the x-axis.<br />
Wh<strong>at</strong> will be the area of the rectangle after these<br />
transform<strong>at</strong>ions?<br />
1) exactly 28 square units<br />
2) less than 28 square units<br />
3) gre<strong>at</strong>er than 28 square units<br />
4) It cannot be determined from the inform<strong>at</strong>ion<br />
given.<br />
310 Wh<strong>at</strong> is the neg<strong>at</strong>ion of the st<strong>at</strong>ement “Squares are<br />
parallelograms”?<br />
1) Parallelograms are squares.<br />
2) Parallelograms are not squares.<br />
3) It is not the case th<strong>at</strong> squares are<br />
parallelograms.<br />
4) It is not the case th<strong>at</strong> parallelograms are<br />
squares.<br />
311 The pentagon in the diagram below is formed by<br />
five rays.<br />
Wh<strong>at</strong> is the degree measure of angle x?<br />
1) 72<br />
2) 96<br />
3) 108<br />
4) 112<br />
312 In the diagram below of ACT, BE → ←⎯⎯<br />
AT.<br />
If CB = 3, CA = 10, and CE = 6, wh<strong>at</strong> is the length<br />
of ET ?<br />
1) 5<br />
2) 14<br />
3) 20<br />
4) 26
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313 The equ<strong>at</strong>ion of a circle is (x − 2) 2 + (y + 4) 2 = 4.<br />
Which diagram is the graph of the circle?<br />
1)<br />
2)<br />
3)<br />
4)<br />
314 In the diagram below of circle O, secant AB<br />
intersects circle O <strong>at</strong> D, secant AOC intersects<br />
circle O <strong>at</strong> E, AE = 4, AB = 12, and DB = 6.<br />
Wh<strong>at</strong> is the length of OC?<br />
1) 4.5<br />
2) 7<br />
3) 9<br />
4) 14<br />
315 In the diagram below of ABC, medians AD, BE ,<br />
and CF intersect <strong>at</strong> G.<br />
If CF = 24, wh<strong>at</strong> is the length of FG?<br />
1) 8<br />
2) 10<br />
3) 12<br />
4) 16
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316 Given: Quadril<strong>at</strong>eral ABCD has vertices A(−5,6),<br />
B(6,6), C(8,−3), and D(−3,−3).<br />
Prove: Quadril<strong>at</strong>eral ABCD is a parallelogram but<br />
is neither a rhombus nor a rectangle. [The use of<br />
the grid below is optional.]<br />
317 A right circular cylinder has an altitude of 11 feet<br />
and a radius of 5 feet. Wh<strong>at</strong> is the l<strong>at</strong>eral area, in<br />
square feet, of the cylinder, to the nearest tenth?<br />
1) 172.7<br />
2) 172.8<br />
3) 345.4<br />
4) 345.6<br />
318 The endpoints of CD are C(−2,−4) and D(6,2).<br />
Wh<strong>at</strong> are the coordin<strong>at</strong>es of the midpoint of CD?<br />
1) (2,3)<br />
2) (2,−1)<br />
3) (4,−2)<br />
4) (4,3)<br />
319 In an equil<strong>at</strong>eral triangle, wh<strong>at</strong> is the difference<br />
between the sum of the exterior angles and the sum<br />
of the interior angles?<br />
1) 180°<br />
2) 120°<br />
3) 90°<br />
4) 60°<br />
320 Using a compass and straightedge, construct a line<br />
th<strong>at</strong> passes through point P and is perpendicular to<br />
line m. [Leave all construction marks.]<br />
321 How many common tangent lines can be drawn to<br />
the two externally tangent circles shown below?<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 4
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322 Wh<strong>at</strong> is the image of point A(4,2) after the<br />
composition of transform<strong>at</strong>ions defined by<br />
R 90° r y = x ?<br />
1) (−4,2)<br />
2) (4,−2)<br />
3) (−4,−2)<br />
4) (2,−4)<br />
323 The rectangle ABCD shown in the diagram below<br />
will be reflected across the x-axis.<br />
Wh<strong>at</strong> will not be preserved?<br />
1) slope of AB<br />
2) parallelism of AB and CD<br />
3) length of AB<br />
4) measure of ∠A<br />
324 If the surface area of a sphere is represented by<br />
144π , wh<strong>at</strong> is the volume in terms of π ?<br />
1) 36π<br />
2) 48π<br />
3) 216π<br />
4) 288π<br />
325 Given: Quadril<strong>at</strong>eral ABCD, diagonal AFEC,<br />
AE ≅ FC , BF ⊥ AC, DE ⊥ AC, ∠1 ≅ ∠2<br />
Prove: ABCD is a parallelogram.<br />
326 The lines 3y + 1 = 6x + 4 and 2y + 1 = x − 9 are<br />
1) parallel<br />
2) perpendicular<br />
3) the same line<br />
4) neither parallel nor perpendicular<br />
327 In the diagram below of circle O, chords AB and<br />
CD intersect <strong>at</strong> E.<br />
If CE = 10, ED = 6, and AE = 4, wh<strong>at</strong> is the length<br />
of EB?<br />
1) 15<br />
2) 12<br />
3) 6.7<br />
4) 2.4
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328 In the diagram below of regular pentagon ABCDE,<br />
EB is drawn.<br />
Wh<strong>at</strong> is the measure of ∠AEB?<br />
1) 36º<br />
2) 54º<br />
3) 72º<br />
4) 108º<br />
329 A regular pyramid with a square base is shown in<br />
the diagram below.<br />
A side, s, of the base of the pyramid is 12 meters,<br />
and the height, h, is 42 meters. Wh<strong>at</strong> is the volume<br />
of the pyramid in cubic meters?<br />
330 The endpoints of PQ are P(−3,1) and Q(4,25).<br />
Find the length of PQ.<br />
331 A transversal intersects two lines. Which condition<br />
would always make the two lines parallel?<br />
1) Vertical angles are congruent.<br />
2) Altern<strong>at</strong>e interior angles are congruent.<br />
3) Corresponding angles are supplementary.<br />
4) Same-side interior angles are complementary.<br />
332 Wh<strong>at</strong> is the neg<strong>at</strong>ion of the st<strong>at</strong>ement “I am not<br />
going to e<strong>at</strong> ice cream”?<br />
1) I like ice cream.<br />
2) I am going to e<strong>at</strong> ice cream.<br />
3) If I e<strong>at</strong> ice cream, then I like ice cream.<br />
4) If I don’t like ice cream, then I don’t e<strong>at</strong> ice<br />
cream.<br />
333 In the diagram below of ADB, m∠BDA = 90,<br />
AD = 5 2, and AB = 2 15.<br />
Wh<strong>at</strong> is the length of BD?<br />
1) 10<br />
2) 20<br />
3) 50<br />
4) 110
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334 Wh<strong>at</strong> is the distance between the points (−3,2) and<br />
(1,0)?<br />
1) 2 2<br />
2) 2 3<br />
3) 5 2<br />
4) 2 5<br />
335 Wh<strong>at</strong> is the contrapositive of the st<strong>at</strong>ement, “If I am<br />
tall, then I will bump my head”?<br />
1) If I bump my head, then I am tall.<br />
2) If I do not bump my head, then I am tall.<br />
3) If I am tall, then I will not bump my head.<br />
4) If I do not bump my head, then I am not tall.<br />
336 In the diagram of circle O below, chord CD is<br />
parallel to diameter AOB and mAC = 30.<br />
Wh<strong>at</strong> is mCD?<br />
1) 150<br />
2) 120<br />
3) 100<br />
4) 60<br />
337 Wh<strong>at</strong> is the equ<strong>at</strong>ion of a line th<strong>at</strong> is parallel to the<br />
line whose equ<strong>at</strong>ion is y = x + 2?<br />
1) x + y = 5<br />
2) 2x + y = −2<br />
3) y − x = −1<br />
4) y − 2x = 3<br />
338 The endpoints of AB are A(3,2) and B(7,1). If<br />
A″B″ is the result of the transform<strong>at</strong>ion of AB<br />
under D 2 T −4,3 wh<strong>at</strong> are the coordin<strong>at</strong>es of A″ and<br />
B″?<br />
1) A″(−2,10) and B″(6,8)<br />
2) A″(−1,5) and B″(3,4)<br />
3) A″(2,7) and B″(10,5)<br />
4) A″(14,−2) and B″(22,−4)<br />
339 In the diagram below, tangent AB and secant ACD<br />
are drawn to circle O from an external point A,<br />
AB = 8, and AC = 4.<br />
Wh<strong>at</strong> is the length of CD?<br />
1) 16<br />
2) 13<br />
3) 12<br />
4) 10
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340 The diagram below shows AB and DE.<br />
Which transform<strong>at</strong>ion will move AB onto DE such<br />
th<strong>at</strong> point D is the image of point A and point E is<br />
the image of point B?<br />
1) T 3,−3<br />
2) D 1<br />
2<br />
3) R 90°<br />
4) r y = x<br />
341 In ABC, AB = 7, BC = 8, and AC = 9. Which<br />
list has the angles of ABC in order from smallest<br />
to largest?<br />
1) ∠A,∠B,∠C<br />
2) ∠B,∠A,∠C<br />
3) ∠C,∠B,∠A<br />
4) ∠C,∠A,∠B<br />
342 In the diagram below, PS is a tangent to circle O <strong>at</strong><br />
point S, PQR is a secant, PS = x, PQ = 3, and<br />
PR = x + 18.<br />
Wh<strong>at</strong> is the length of PS ?<br />
1) 6<br />
2) 9<br />
3) 3<br />
4) 27<br />
343 Wh<strong>at</strong> is the slope of a line perpendicular to the line<br />
whose equ<strong>at</strong>ion is 2y = −6x + 8?<br />
1) −3<br />
1<br />
2)<br />
6<br />
3)<br />
1<br />
3<br />
4) −6<br />
344 Given: Quadril<strong>at</strong>eral ABCD with AB ≅ CD,<br />
AD ≅ BC , and diagonal BD is drawn<br />
Prove: ∠BDC ≅ ∠ABD
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345 Wh<strong>at</strong> is the converse of the st<strong>at</strong>ement "If Bob does<br />
his homework, then George gets candy"?<br />
1) If George gets candy, then Bob does his<br />
homework.<br />
2) Bob does his homework if and only if George<br />
gets candy.<br />
3) If George does not get candy, then Bob does<br />
not do his homework.<br />
4) If Bob does not do his homework, then George<br />
does not get candy.<br />
346 In the diagram below of circle C, QR is a diameter,<br />
and Q(1,8) and C(3.5,2) are points on a coordin<strong>at</strong>e<br />
plane. Find and st<strong>at</strong>e the coordin<strong>at</strong>es of point R.<br />
347 The lines represented by the equ<strong>at</strong>ions y + 1<br />
x = 4<br />
2<br />
and 3x + 6y = 12 are<br />
1) the same line<br />
2) parallel<br />
3) perpendicular<br />
4) neither parallel nor perpendicular<br />
348 In the diagram of ABC and DEF below,<br />
AB ≅ DE, ∠A ≅ ∠D, and ∠B ≅ ∠E.<br />
Which method can be used to prove<br />
ABC ≅ DEF?<br />
1) SSS<br />
2) SAS<br />
3) ASA<br />
4) HL<br />
349 The diameter of a circle has endpoints <strong>at</strong> (−2,3) and<br />
(6,3). Wh<strong>at</strong> is an equ<strong>at</strong>ion of the circle?<br />
1) (x − 2) 2 + (y − 3) 2 = 16<br />
2) (x − 2) 2 + (y − 3) 2 = 4<br />
3) (x + 2) 2 + (y + 3) 2 = 16<br />
4) (x + 2) 2 + (y + 3) 2 = 4<br />
350 Wh<strong>at</strong> is an equ<strong>at</strong>ion of the line th<strong>at</strong> passes through<br />
the point (7,3) and is parallel to the line<br />
4x + 2y = 10?<br />
1) y = 1 1<br />
x −<br />
2 2<br />
2) y = − 1 13<br />
x +<br />
2 2<br />
3) y = 2x − 11<br />
4) y = −2x + 17
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351 Side PQ of PQR is extended through Q to point<br />
T. Which st<strong>at</strong>ement is not always true?<br />
1) m∠RQT > m∠R<br />
2) m∠RQT > m∠P<br />
3) m∠RQT = m∠P + m∠R<br />
4) m∠RQT > m∠PQR<br />
352 Juliann plans on drawing ABC, where the<br />
measure of ∠A can range from 50° to 60° and the<br />
measure of ∠B can range from 90° to 100°. Given<br />
these conditions, wh<strong>at</strong> is the correct range of<br />
measures possible for ∠C?<br />
1) 20° to 40°<br />
2) 30° to 50°<br />
3) 80° to 90°<br />
4) 120° to 130°<br />
353 In the diagram below, the length of the legs AC and<br />
BC of right triangle ABC are 6 cm and 8 cm,<br />
respectively. Altitude CD is drawn to the<br />
hypotenuse of ABC.<br />
Wh<strong>at</strong> is the length of AD to the nearest tenth of a<br />
centimeter?<br />
1) 3.6<br />
2) 6.0<br />
3) 6.4<br />
4) 4.0<br />
354 The equ<strong>at</strong>ion of a circle is x 2 + (y − 7) 2 = 16. Wh<strong>at</strong><br />
are the center and radius of the circle?<br />
1) center = (0,7); radius = 4<br />
2) center = (0,7); radius = 16<br />
3) center = (0,−7); radius = 4<br />
4) center = (0,−7); radius = 16<br />
355 In the diagram below of TEM , medians TB, EC ,<br />
and MA intersect <strong>at</strong> D, and TB = 9. Find the length<br />
of TD.<br />
356 In the diagram below of ABC with side AC<br />
extended through D, m∠A = 37 and<br />
m∠BCD = 117. Which side of ABC is the<br />
longest side? Justify your answer.
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357 In the diagram below, the vertices of DEF are<br />
the midpoints of the sides of equil<strong>at</strong>eral triangle<br />
ABC, and the perimeter of ABC is 36 cm.<br />
Wh<strong>at</strong> is the length, in centimeters, of EF?<br />
1) 6<br />
2) 12<br />
3) 18<br />
4) 4<br />
358 The diagram below shows a pennant in the shape of<br />
an isosceles triangle. The equal sides each measure<br />
13, the altitude is x + 7, and the base is 2x.<br />
Wh<strong>at</strong> is the length of the base?<br />
1) 5<br />
2) 10<br />
3) 12<br />
4) 24<br />
359 A city is planning to build a new park. The park<br />
must be equidistant from school A <strong>at</strong> (3,3) and<br />
school B <strong>at</strong> (3,−5). The park also must be exactly 5<br />
miles from the center of town, which is loc<strong>at</strong>ed <strong>at</strong><br />
the origin on the coordin<strong>at</strong>e graph. Each unit on the<br />
graph represents 1 mile. On the set of axes below,<br />
sketch the compound loci and label with an X all<br />
possible loc<strong>at</strong>ions for the new park.<br />
360 If the diagonals of a quadril<strong>at</strong>eral do not bisect<br />
each other, then the quadril<strong>at</strong>eral could be a<br />
1) rectangle<br />
2) rhombus<br />
3) square<br />
4) trapezoid
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361 In the diagram below of ABC, D is a point on<br />
AB, AC = 7, AD = 6, and BC = 18.<br />
The length of DB could be<br />
1) 5<br />
2) 12<br />
3) 19<br />
4) 25<br />
362 The diagram below illustr<strong>at</strong>es the construction of<br />
PS → ←⎯<br />
parallel to RQ → ←⎯⎯<br />
through point P.<br />
Which st<strong>at</strong>ement justifies this construction?<br />
1) m∠1 = m∠2<br />
2) m∠1 = m∠3<br />
3) PR ≅ RQ<br />
4) PS ≅ RQ<br />
363 Which graph represents a circle with the equ<strong>at</strong>ion<br />
(x − 5) 2 + (y + 1) 2 = 9?<br />
1)<br />
2)<br />
3)<br />
4)
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364 A circle is represented by the equ<strong>at</strong>ion<br />
x 2 + (y + 3) 2 = 13. Wh<strong>at</strong> are the coordin<strong>at</strong>es of the<br />
center of the circle and the length of the radius?<br />
1) (0,3) and 13<br />
2) (0,3) and 13<br />
3) (0,−3) and 13<br />
4) (0,−3) and 13<br />
365 The vertices of ABC are A(−1,−2), B(−1,2) and<br />
C(6,0). Which conclusion can be made about the<br />
angles of ABC?<br />
1) m∠A = m∠B<br />
2) m∠A = m∠C<br />
3) m∠ACB = 90<br />
4) m∠ABC = 60<br />
366 Which expression represents the volume, in cubic<br />
centimeters, of the cylinder represented in the<br />
diagram below?<br />
1) 162π<br />
2) 324π<br />
3) 972π<br />
4) 3,888π<br />
367 Wh<strong>at</strong> is the length of the line segment with<br />
endpoints (−6,4) and (2,−5)?<br />
1) 13<br />
2) 17<br />
3) 72<br />
4) 145<br />
368 In the diagram below of ABC, AE ≅ BE ,<br />
AF ≅ CF, and CD ≅ BD.<br />
Point P must be the<br />
1) centroid<br />
2) circumcenter<br />
3) Incenter<br />
4) orthocenter<br />
369 In PQR, PQ = 8, QR = 12, and RP = 13. Which<br />
st<strong>at</strong>ement about the angles of PQR must be true?<br />
1) m∠Q > m∠P > m∠R<br />
2) m∠Q > m∠R > m∠P<br />
3) m∠R > m∠P > m∠Q<br />
4) m∠P > m∠R > m∠Q
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370 Based on the diagram below, which st<strong>at</strong>ement is<br />
true?<br />
1) a b<br />
2) a c<br />
3) b c<br />
4) d e<br />
371 In the diagram below of ACD, E is a point on<br />
AD and B is a point on AC, such th<strong>at</strong> EB DC . If<br />
AE = 3, ED = 6, and DC = 15, find the length of<br />
EB.<br />
372 In three-dimensional space, two planes are parallel<br />
and a third plane intersects both of the parallel<br />
planes. The intersection of the planes is a<br />
1) plane<br />
2) point<br />
3) pair of parallel lines<br />
4) pair of intersecting lines<br />
373 In the diagram below of right triangle ACB, altitude<br />
CD intersects AB <strong>at</strong> D. If AD = 3 and DB = 4, find<br />
the length of CD in simplest radical form.<br />
374 In the diagram below of ABC, CD is the bisector<br />
of ∠BCA, AE is the bisector of ∠CAB, and BG is<br />
drawn.<br />
Which st<strong>at</strong>ement must be true?<br />
1) DG = EG<br />
2) AG = BG<br />
3) ∠AEB ≅ ∠AEC<br />
4) ∠DBG ≅ ∠EBG
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375 Which transform<strong>at</strong>ion produces a figure similar but<br />
not congruent to the original figure?<br />
1) T1,3 2) D 1<br />
2<br />
3) R90° 4) r y = x<br />
376 In the diagram of ABC below, AB ≅ AC. The<br />
measure of ∠B is 40°.<br />
Wh<strong>at</strong> is the measure of ∠A?<br />
1) 40°<br />
2) 50°<br />
3) 70°<br />
4) 100°<br />
377 The base of a pyramid is a rectangle with a width<br />
of 6 cm and a length of 8 cm. Find, in centimeters,<br />
the height of the pyramid if the volume is 288 cm 3 .<br />
378 Wh<strong>at</strong> is an equ<strong>at</strong>ion for the circle shown in the<br />
graph below?<br />
1) x 2 + y 2 = 2<br />
2) x 2 + y 2 = 4<br />
3) x 2 + y 2 = 8<br />
4) x 2 + y 2 = 16<br />
379 Isosceles trapezoid ABCD has diagonals AC and<br />
BD. If AC = 5x + 13 and BD = 11x − 5, wh<strong>at</strong> is the<br />
value of x?<br />
1) 28<br />
2) 10 3<br />
4<br />
3) 3<br />
4)<br />
1<br />
2
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380 On the set of axes below, solve the following<br />
system of equ<strong>at</strong>ions graphically for all values of x<br />
and y.<br />
y = (x − 2) 2 + 4<br />
4x + 2y = 14<br />
381 Wh<strong>at</strong> is the slope of a line th<strong>at</strong> is perpendicular to<br />
the line whose equ<strong>at</strong>ion is 3x + 4y = 12?<br />
1)<br />
3<br />
4<br />
2) − 3<br />
4<br />
3)<br />
4<br />
3<br />
4) − 4<br />
3<br />
382 Point A is not contained in plane B. How many<br />
lines can be drawn through point A th<strong>at</strong> will be<br />
perpendicular to plane B?<br />
1) one<br />
2) two<br />
3) zero<br />
4) infinite<br />
383 A polygon is transformed according to the rule:<br />
(x,y) → (x + 2,y). Every point of the polygon<br />
moves two units in which direction?<br />
1) up<br />
2) down<br />
3) left<br />
4) right<br />
384 In the diagram of circle O below, chord AB<br />
intersects chord CD <strong>at</strong> E, DE = 2x + 8, EC = 3,<br />
AE = 4x − 3, and EB = 4.<br />
Wh<strong>at</strong> is the value of x?<br />
1) 1<br />
2) 3.6<br />
3) 5<br />
4) 10.25
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385 A rectangular prism has a volume of<br />
3x 2 + 18x + 24. Its base has a length of x + 2 and a<br />
width of 3. Which expression represents the height<br />
of the prism?<br />
1) x + 4<br />
2) x + 2<br />
3) 3<br />
4) x 2 + 6x + 8<br />
386 The diagram below shows the construction of the<br />
bisector of ∠ABC.<br />
Which st<strong>at</strong>ement is not true?<br />
1) m∠EBF = 1<br />
2 m∠ABC<br />
2) m∠DBF = 1<br />
2 m∠ABC<br />
3) m∠EBF = m∠ABC<br />
4) m∠DBF = m∠EBF<br />
387 Using a compass and straightedge, construct the<br />
bisector of the angle shown below. [Leave all<br />
construction marks.]<br />
388 The diagram below shows the construction of the<br />
perpendicular bisector of AB.<br />
Which st<strong>at</strong>ement is not true?<br />
1) AC = CB<br />
2) CB = 1<br />
2 AB<br />
3) AC = 2AB<br />
4) AC + CB = AB
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389 In the diagram below of isosceles trapezoid DEFG,<br />
DE GF, DE = 4x − 2, EF = 3x + 2, FG = 5x − 3,<br />
and GD = 2x + 5. Find the value of x.<br />
390 Write an equ<strong>at</strong>ion for circle O shown on the graph<br />
below.<br />
391 Wh<strong>at</strong> is an equ<strong>at</strong>ion of the line th<strong>at</strong> contains the<br />
point (3,−1) and is perpendicular to the line whose<br />
equ<strong>at</strong>ion is y = −3x + 2?<br />
1) y = −3x + 8<br />
2) y = −3x<br />
3) y = 1<br />
3 x<br />
4) y = 1<br />
x − 2<br />
3<br />
392 After a composition of transform<strong>at</strong>ions, the<br />
coordin<strong>at</strong>es A(4,2), B(4,6), and C(2,6) become<br />
A″(−2,−1), B″(−2,−3), and C ″(−1,−3), as shown on<br />
the set of axes below.<br />
Which composition of transform<strong>at</strong>ions was used?<br />
1) R180° D 2<br />
2) R90° D 2<br />
3) D 1<br />
2<br />
R180° 4) D 1<br />
2<br />
R90°
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393 The diagram below shows the construction of a line<br />
through point P perpendicular to line m.<br />
Which st<strong>at</strong>ement is demonstr<strong>at</strong>ed by this<br />
construction?<br />
1) If a line is parallel to a line th<strong>at</strong> is<br />
perpendicular to a third line, then the line is<br />
also perpendicular to the third line.<br />
2) The set of points equidistant from the<br />
endpoints of a line segment is the<br />
perpendicular bisector of the segment.<br />
3) Two lines are perpendicular if they are<br />
equidistant from a given point.<br />
4) Two lines are perpendicular if they intersect to<br />
form a vertical line.<br />
394 Tangents PA and PB are drawn to circle O from an<br />
external point, P, and radii OA and OB are drawn.<br />
If m∠APB = 40, wh<strong>at</strong> is the measure of ∠AOB?<br />
1) 140º<br />
2) 100º<br />
3) 70º<br />
4) 50º<br />
395 A transform<strong>at</strong>ion of a polygon th<strong>at</strong> always<br />
preserves both length and orient<strong>at</strong>ion is<br />
1) dil<strong>at</strong>ion<br />
2) transl<strong>at</strong>ion<br />
3) line reflection<br />
4) glide reflection<br />
396 Wh<strong>at</strong> is the length, to the nearest tenth, of the line<br />
segment joining the points (−4,2) and (146,52)?<br />
1) 141.4<br />
2) 150.5<br />
3) 151.9<br />
4) 158.1<br />
397 Which equ<strong>at</strong>ion represents circle K shown in the<br />
graph below?<br />
1) (x + 5) 2 + (y − 1) 2 = 3<br />
2) (x + 5) 2 + (y − 1) 2 = 9<br />
3) (x − 5) 2 + (y + 1) 2 = 3<br />
4) (x − 5) 2 + (y + 1) 2 = 9
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398 Two lines are represented by the equ<strong>at</strong>ions<br />
− 1<br />
y = 6x + 10 and y = mx. For which value of m<br />
2<br />
will the lines be parallel?<br />
1) −12<br />
2) −3<br />
3) 3<br />
4) 12<br />
399 In the diagram below, ABC is inscribed in circle<br />
P. The distances from the center of circle P to each<br />
side of the triangle are shown.<br />
Which st<strong>at</strong>ement about the sides of the triangle is<br />
true?<br />
1) AB > AC > BC<br />
2) AB < AC and AC > BC<br />
3) AC > AB > BC<br />
4) AC = AB and AB > BC<br />
400 In isosceles trapezoid ABCD, AB ≅ CD. If<br />
BC = 20, AD = 36, and AB = 17, wh<strong>at</strong> is the length<br />
of the altitude of the trapezoid?<br />
1) 10<br />
2) 12<br />
3) 15<br />
4) 16<br />
401 Find an equ<strong>at</strong>ion of the line passing through the<br />
point (6,5) and perpendicular to the line whose<br />
equ<strong>at</strong>ion is 2y + 3x = 6.<br />
402 In the diagram below, circle A and circle B are<br />
shown.<br />
Wh<strong>at</strong> is the total number of lines of tangency th<strong>at</strong><br />
are common to circle A and circle B?<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 4<br />
403 Given ABC ∼ DEF such th<strong>at</strong> AB 3<br />
= . Which<br />
DE 2<br />
st<strong>at</strong>ement is not true?<br />
1)<br />
BC 3<br />
=<br />
EF 2<br />
2) m∠A 3<br />
=<br />
m∠D 2<br />
3)<br />
area of<br />
area of<br />
ABC 9<br />
=<br />
DEF 4<br />
4)<br />
perimeter of<br />
perimeter of<br />
ABC 3<br />
=<br />
DEF 2
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404 In the diagram below, ABC ∼ EFG,<br />
m∠C = 4x + 30, and m∠G = 5x + 10. Determine<br />
the value of x.<br />
405 If the endpoints of AB are A(−4,5) and B(2,−5),<br />
wh<strong>at</strong> is the length of AB?<br />
1) 2 34<br />
2) 2<br />
3) 61<br />
4) 8<br />
406 The diagonal AC is drawn in parallelogram ABCD.<br />
Which method can not be used to prove th<strong>at</strong><br />
ABC ≅ CDA?<br />
1) SSS<br />
2) SAS<br />
3) SSA<br />
4) ASA<br />
407 In ABC, point D is on AB, and point E is on BC<br />
such th<strong>at</strong> DE AC. If DB = 2, DA = 7, and<br />
DE = 3, wh<strong>at</strong> is the length of AC?<br />
1) 8<br />
2) 9<br />
3) 10.5<br />
4) 13.5<br />
408 Which transform<strong>at</strong>ion of the line x = 3 results in an<br />
image th<strong>at</strong> is perpendicular to the given line?<br />
1) r x-axis<br />
2) r y-axis<br />
3) r y = x<br />
4) r x = 1<br />
409 Given: y = 1<br />
x − 3<br />
4<br />
y = x 2 + 8x + 12<br />
In which quadrant will the graphs of the given<br />
equ<strong>at</strong>ions intersect?<br />
1) I<br />
2) II<br />
3) III<br />
4) IV<br />
410 In plane P, lines m and n intersect <strong>at</strong> point A. If<br />
line k is perpendicular to line m and line n <strong>at</strong> point<br />
A, then line k is<br />
1) contained in plane P<br />
2) parallel to plane P<br />
3) perpendicular to plane P<br />
4) skew to plane P
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411 Two lines, AB → ←⎯<br />
and CRD → ←⎯⎯⎯<br />
, are parallel and 10<br />
inches apart. Sketch the locus of all points th<strong>at</strong> are<br />
equidistant from AB → ←⎯<br />
and CRD → ←⎯⎯⎯<br />
and 7 inches from<br />
point R. Label with an X each point th<strong>at</strong> s<strong>at</strong>isfies<br />
both conditions.<br />
412 In which triangle do the three altitudes intersect<br />
outside the triangle?<br />
1) a right triangle<br />
2) an acute triangle<br />
3) an obtuse triangle<br />
4) an equil<strong>at</strong>eral triangle<br />
413 One step in a construction uses the endpoints of AB<br />
to cre<strong>at</strong>e arcs with the same radii. The arcs<br />
intersect above and below the segment. Wh<strong>at</strong> is<br />
the rel<strong>at</strong>ionship of AB and the line connecting the<br />
points of intersection of these arcs?<br />
1) collinear<br />
2) congruent<br />
3) parallel<br />
4) perpendicular<br />
414 Given the equ<strong>at</strong>ions: y = x 2 − 6x + 10<br />
y + x = 4<br />
Wh<strong>at</strong> is the solution to the given system of<br />
equ<strong>at</strong>ions?<br />
1) (2,3)<br />
2) (3,2)<br />
3) (2,2) and (1,3)<br />
4) (2,2) and (3,1)<br />
415 Square LMNO is shown in the diagram below.<br />
Wh<strong>at</strong> are the coordin<strong>at</strong>es of the midpoint of<br />
diagonal LN ?<br />
1) 4 1 <br />
1 <br />
,−2<br />
2 2 <br />
2) −3 1 <br />
1 <br />
,3<br />
2 2 <br />
3) −2 1 <br />
1 <br />
,3<br />
2 2 <br />
4) −2 1 <br />
1 <br />
,4<br />
2 2
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416 In the diagram below of PRT, Q is a point on<br />
PR, S is a point on TR, QS is drawn, and<br />
∠RPT ≅ ∠RSQ.<br />
Which reason justifies the conclusion th<strong>at</strong><br />
PRT ∼ SRQ?<br />
1) AA<br />
2) ASA<br />
3) SAS<br />
4) SSS<br />
417 On the line segment below, use a compass and<br />
straightedge to construct equil<strong>at</strong>eral triangle ABC.<br />
[Leave all construction marks.]<br />
418 Which geometric principle is used in the<br />
construction shown below?<br />
1) The intersection of the angle bisectors of a<br />
triangle is the center of the inscribed circle.<br />
2) The intersection of the angle bisectors of a<br />
triangle is the center of the circumscribed<br />
circle.<br />
3) The intersection of the perpendicular bisectors<br />
of the sides of a triangle is the center of the<br />
inscribed circle.<br />
4) The intersection of the perpendicular bisectors<br />
of the sides of a triangle is the center of the<br />
circumscribed circle.<br />
419 Which set of numbers represents the lengths of the<br />
sides of a triangle?<br />
1) {5,18,13}<br />
2) {6,17,22}<br />
3) {16,24,7}<br />
4) {26,8,15}
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420 Write an equ<strong>at</strong>ion of the circle whose diameter AB<br />
has endpoints A(−4,2) and B(4,−4). [The use of<br />
the grid below is optional.]<br />
421 In the diagram of ABC below, AB = 10, BC = 14,<br />
and AC = 16. Find the perimeter of the triangle<br />
formed by connecting the midpoints of the sides of<br />
ABC.<br />
422 Wh<strong>at</strong> is the slope of a line perpendicular to the line<br />
whose equ<strong>at</strong>ion is 5x + 3y = 8?<br />
1)<br />
5<br />
3<br />
2)<br />
3<br />
5<br />
3) − 3<br />
5<br />
4) − 5<br />
3<br />
423 Using a compass and straightedge, construct the<br />
angle bisector of ∠ABC shown below. [Leave all<br />
construction marks.]
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424 In the diagram below, a right circular cone has a<br />
diameter of 8 inches and a height of 12 inches.<br />
Wh<strong>at</strong> is the volume of the cone to the nearest cubic<br />
inch?<br />
1) 201<br />
2) 481<br />
3) 603<br />
4) 804<br />
425 In which polygon does the sum of the measures of<br />
the interior angles equal the sum of the measures of<br />
the exterior angles?<br />
1) triangle<br />
2) hexagon<br />
3) octagon<br />
4) quadril<strong>at</strong>eral<br />
426 Wh<strong>at</strong> is the slope of a line perpendicular to the line<br />
whose equ<strong>at</strong>ion is y = 3x + 4?<br />
1)<br />
1<br />
3<br />
2) − 1<br />
3<br />
3) 3<br />
4) −3<br />
427 Which equ<strong>at</strong>ion represents a line perpendicular to<br />
the line whose equ<strong>at</strong>ion is 2x + 3y = 12?<br />
1) 6y = −4x + 12<br />
2) 2y = 3x + 6<br />
3) 2y = −3x + 6<br />
4) 3y = −2x + 12<br />
428 ABC is similar to DEF. The r<strong>at</strong>io of the<br />
length of AB to the length of DE is 3:1. Which<br />
r<strong>at</strong>io is also equal to 3:1?<br />
1) m∠A<br />
m∠D<br />
2) m∠B<br />
m∠F<br />
3)<br />
area of ABC<br />
4)<br />
area of DEF<br />
perimeter of ABC<br />
perimeter of DEF<br />
429 The figure in the diagram below is a triangular<br />
prism.<br />
Which st<strong>at</strong>ement must be true?<br />
1) DE ≅ AB<br />
2) AD ≅ BC<br />
3) AD CE<br />
4) DE BC
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430 In ABC, m∠A = 95, m∠B = 50, and m∠C = 35.<br />
Which expression correctly rel<strong>at</strong>es the lengths of<br />
the sides of this triangle?<br />
1) AB < BC < CA<br />
2) AB < AC < BC<br />
3) AC < BC < AB<br />
4) BC < AC < AB<br />
431 Triangle DEG has the coordin<strong>at</strong>es D(1,1), E(5,1),<br />
and G(5,4). Triangle DEG is rot<strong>at</strong>ed 90° about the<br />
origin to form D′E ′G′. On the grid below, graph<br />
and label DEG and D′E ′G′. St<strong>at</strong>e the<br />
coordin<strong>at</strong>es of the vertices D', E', and G'. Justify<br />
th<strong>at</strong> this transform<strong>at</strong>ion preserves distance.<br />
432 Which diagram shows the construction of an<br />
equil<strong>at</strong>eral triangle?<br />
1)<br />
2)<br />
3)<br />
4)
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433 In the diagram below of trapezoid RSUT, RS TU ,<br />
X is the midpoint of RT , and V is the midpoint of<br />
SU .<br />
If RS = 30 and XV = 44, wh<strong>at</strong> is the length of TU ?<br />
1) 37<br />
2) 58<br />
3) 74<br />
4) 118<br />
434 In the diagram of trapezoid ABCD below, diagonals<br />
AC and BD intersect <strong>at</strong> E and ABC ≅ DCB.<br />
Which st<strong>at</strong>ement is true based on the given<br />
inform<strong>at</strong>ion?<br />
1) AC ≅ BC<br />
2) CD ≅ AD<br />
3) ∠CDE ≅ ∠BAD<br />
4) ∠CDB ≅ ∠BAC<br />
435 Point A is loc<strong>at</strong>ed <strong>at</strong> (4,−7). The point is reflected<br />
in the x-axis. Its image is loc<strong>at</strong>ed <strong>at</strong><br />
1) (−4,7)<br />
2) (−4,−7)<br />
3) (4,7)<br />
4) (7,−4)<br />
436 In the diagram below, ABC is shown with AC<br />
extended through point D.<br />
If m∠BCD = 6x + 2, m∠BAC = 3x + 15, and<br />
m∠ABC = 2x − 1, wh<strong>at</strong> is the value of x?<br />
1) 12<br />
2) 14 10<br />
11<br />
3) 16<br />
4) 18 1<br />
9<br />
437 The degree measures of the angles of ABC are<br />
represented by x, 3x, and 5x − 54. Find the value of<br />
x.
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 86 NAME:________________________________<br />
www.jmap.org<br />
438 In the diagram of ABC below, Jose found<br />
centroid P by constructing the three medians. He<br />
measured CF and found it to be 6 inches.<br />
If PF = x, which equ<strong>at</strong>ion can be used to find x?<br />
1) x + x = 6<br />
2) 2x + x = 6<br />
3) 3x + 2x = 6<br />
4) x + 2<br />
x = 6<br />
3<br />
439 Towns A and B are 16 miles apart. How many<br />
points are 10 miles from town A and 12 miles from<br />
town B?<br />
1) 1<br />
2) 2<br />
3) 3<br />
4) 0<br />
440 The volume of a cylinder is 12,566.4 cm 3 . The<br />
height of the cylinder is 8 cm. Find the radius of<br />
the cylinder to the nearest tenth of a centimeter.<br />
441 A support beam between the floor and ceiling of a<br />
house forms a 90º angle with the floor. The builder<br />
wants to make sure th<strong>at</strong> the floor and ceiling are<br />
parallel. Which angle should the support beam<br />
form with the ceiling?<br />
1) 45º<br />
2) 60º<br />
3) 90º<br />
4) 180º<br />
442 Which equ<strong>at</strong>ion represents a line parallel to the line<br />
whose equ<strong>at</strong>ion is 2y − 5x = 10?<br />
1) 5y − 2x = 25<br />
2) 5y + 2x = 10<br />
3) 4y − 10x = 12<br />
4) 2y + 10x = 8<br />
443 Point P is on line m. Wh<strong>at</strong> is the total number of<br />
planes th<strong>at</strong> are perpendicular to line m and pass<br />
through point P?<br />
1) 1<br />
2) 2<br />
3) 0<br />
4) infinite
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 87 NAME:________________________________<br />
www.jmap.org<br />
444 Using a compass and straightedge, on the diagram<br />
below of RS → ←⎯<br />
, construct an equil<strong>at</strong>eral triangle with<br />
RS as one side. [Leave all construction marks.]<br />
445 In the diagram below of circle O, chords DF, DE,<br />
FG, and EG are drawn such th<strong>at</strong><br />
mDF :mFE :mEG :mGD = 5:2:1:7. Identify one<br />
pair of inscribed angles th<strong>at</strong> are congruent to each<br />
other and give their measure.<br />
446 In the diagram below, SQ and PR intersect <strong>at</strong> T,<br />
PQ is drawn, and PS QR.<br />
Wh<strong>at</strong> technique can be used to prove th<strong>at</strong><br />
PST ∼ RQT?<br />
1) SAS<br />
2) SSS<br />
3) ASA<br />
4) AA<br />
447 Which equ<strong>at</strong>ion represents the circle whose center<br />
is (−2,3) and whose radius is 5?<br />
1) (x − 2) 2 + (y + 3) 2 = 5<br />
2) (x + 2) 2 + (y − 3) 2 = 5<br />
3) (x + 2) 2 + (y − 3) 2 = 25<br />
4) (x − 2) 2 + (y + 3) 2 = 25
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 88 NAME:________________________________<br />
www.jmap.org<br />
448 In the diagram below of parallelogram ABCD with<br />
diagonals AC and BD, m∠1 = 45 and<br />
m∠DCB = 120.<br />
Wh<strong>at</strong> is the measure of ∠2?<br />
1) 15º<br />
2) 30º<br />
3) 45º<br />
4) 60º<br />
449 Triangle ABC has vertices A(1,3), B(0,1), and<br />
C(4,0). Under a transl<strong>at</strong>ion, A′, the image point of<br />
A, is loc<strong>at</strong>ed <strong>at</strong> (4,4). Under this same transl<strong>at</strong>ion,<br />
point C ′ is loc<strong>at</strong>ed <strong>at</strong><br />
1) (7,1)<br />
2) (5,3)<br />
3) (3,2)<br />
4) (1,−1)<br />
450 Given: JKLM is a parallelogram.<br />
JM ≅ LN<br />
∠LMN ≅ ∠LNM<br />
Prove: JKLM is a rhombus.<br />
451 Wh<strong>at</strong> is the neg<strong>at</strong>ion of the st<strong>at</strong>ement “The Sun is<br />
shining”?<br />
1) It is cloudy.<br />
2) It is daytime.<br />
3) It is not raining.<br />
4) The Sun is not shining.<br />
452 In the diagram below, under which transform<strong>at</strong>ion<br />
will A′B′C ′ be the image of ABC?<br />
1) rot<strong>at</strong>ion<br />
2) dil<strong>at</strong>ion<br />
3) transl<strong>at</strong>ion<br />
4) glide reflection<br />
453 Line segment AB is tangent to circle O <strong>at</strong> A. Which<br />
type of triangle is always formed when points A, B,<br />
and O are connected?<br />
1) right<br />
2) obtuse<br />
3) scalene<br />
4) isosceles
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 89 NAME:________________________________<br />
www.jmap.org<br />
454 Which illustr<strong>at</strong>ion shows the correct construction<br />
of an angle bisector?<br />
1)<br />
2)<br />
3)<br />
4)<br />
455 Which graph could be used to find the solution to<br />
the following system of equ<strong>at</strong>ions?<br />
y = −x + 2<br />
1)<br />
2)<br />
3)<br />
4)<br />
y = x 2
<strong>Geometry</strong> <strong>Regents</strong> Exam Questions <strong>at</strong> <strong>Random</strong> Worksheet # 90 NAME:________________________________<br />
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456 The length of AB is 3 inches. On the diagram below, sketch the points th<strong>at</strong> are equidistant from A and B and<br />
sketch the points th<strong>at</strong> are 2 inches from A. Label with an X all points th<strong>at</strong> s<strong>at</strong>isfy both conditions.
<strong>Geometry</strong> <strong>Regents</strong> <strong>at</strong> <strong>Random</strong> <strong>Worksheets</strong><br />
Answer Section<br />
1 ANS:<br />
PTS: 4 REF: 061137ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
2 ANS: 4<br />
d = (−5 − 3) 2 + (4 − (−6)) 2 = 64 + 100 = 164 = 4 41 = 2 41<br />
PTS: 2<br />
KEY: general<br />
REF: 011121ge STA: G.G.67 TOP: Distance<br />
3 ANS: 1<br />
TOP: Neg<strong>at</strong>ions<br />
4 ANS: 1<br />
PTS: 2 REF: 011213ge STA: G.G.24<br />
3x + 5 + 4x − 15 + 2x + 10 = 180.<br />
m∠D = 3(20) + 5 = 65. m∠E = 4(20) − 15 = 65.<br />
9x = 180<br />
x = 20<br />
ID: A<br />
PTS: 2 REF: 061119ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles<br />
5 ANS:<br />
Quadril<strong>at</strong>eral ABCD, AD ≅ BC and ∠DAE ≅ ∠BCE are given. AD BC because if two lines are cut by a<br />
transversal so th<strong>at</strong> a pair of altern<strong>at</strong>e interior angles are congruent, the lines are parallel. ABCD is a parallelogram<br />
because if one pair of opposite sides of a quadril<strong>at</strong>eral are both congruent and parallel, the quadril<strong>at</strong>eral is a<br />
parallelogram. AE ≅ CE because the diagonals of a parallelogram bisect each other. ∠FEA ≅ ∠GEC as vertical<br />
angles. AEF ≅ CEG by ASA.<br />
PTS: 6 REF: 011238ge STA: G.G.27 TOP: Quadril<strong>at</strong>eral Proofs<br />
6 ANS: 2 PTS: 2 REF: 011215ge STA: G.G.12<br />
TOP: Volume
7 ANS:<br />
30.<br />
PTS: 2 REF: 011129ge STA: G.G.31 TOP: Isosceles Triangle Theorem<br />
8 ANS: 3 PTS: 2 REF: 061122ge STA: G.G.56<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
9 ANS: 3<br />
TOP: Solids<br />
PTS: 2 REF: 011105ge STA: G.G.10<br />
10 ANS: 4 PTS: 2 REF: 081106ge STA: G.G.17<br />
TOP: Constructions<br />
11 ANS: 3 PTS: 2 REF: 061220ge STA: G.G.74<br />
TOP: Graphing Circles<br />
12 ANS:<br />
16.7. x 12<br />
=<br />
25 18<br />
18x = 300<br />
x ≈ 16.7<br />
PTS: 2 REF: 061133ge STA: G.G.46 TOP: Side Splitter Theorem<br />
13 ANS:<br />
PTS: 2 REF: 081233ge STA: G.G.19 TOP: Constructions<br />
14 ANS: 2<br />
The slope of a line in standard form is −A<br />
B<br />
ID: A<br />
−4<br />
, so the slope of this line is . A parallel line would also have a slope<br />
3<br />
of −4<br />
. Since the answers are in standard form, use the point-slope formula. y − 2 = −4 (x + 5)<br />
3 3<br />
3y − 6 = −4x − 20<br />
4x + 3y = −14<br />
PTS: 2<br />
15 ANS:<br />
REF: 061123ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
L = 2πrh = 2π ⋅ 12 ⋅ 22 ≈ 1659. 1659<br />
≈ 2.8. 3 cans are needed.<br />
600<br />
PTS: 2 REF: 061233ge STA: G.G.14 TOP: L<strong>at</strong>eral Area
16 ANS: 1<br />
<br />
8 + 0<br />
m =<br />
2<br />
, 2 + 6<br />
2<br />
<br />
<br />
6 − 2 4<br />
= (4,4) m = = = −1<br />
0 − 8 −8 2 m⊥ = 2 y = mx + b<br />
4 = 2(4) + b<br />
−4 = b<br />
PTS: 2<br />
17 ANS: 4<br />
m⊥ = −<br />
REF: 081126ge STA: G.G.68 TOP: Perpendicular Bisector<br />
1<br />
. y = mx + b<br />
3<br />
6 = − 1<br />
(−9) + b<br />
3<br />
6 = 3 + b<br />
3 = b<br />
PTS: 2 REF: 061215ge STA: G.G.64 TOP: Parallel and Perpendicular Lines<br />
18 ANS:<br />
PTS: 2 REF: 011130ge STA: G.G.54 TOP: Reflections<br />
KEY: grids<br />
19 ANS: 2<br />
7x = 5x + 30<br />
2x = 30<br />
x = 15<br />
PTS: 2<br />
20 ANS:<br />
REF: 061106ge STA: G.G.35 TOP: Parallel Lines and Transversals<br />
(5 − 2)180 = 540. 540<br />
= 108 interior. 180 − 108 = 72 exterior<br />
5<br />
ID: A<br />
PTS: 2 REF: 011131ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons<br />
21 ANS: 2 PTS: 2 REF: 081102ge STA: G.G.29<br />
TOP: Triangle Congruency<br />
22 ANS: 3 PTS: 2 REF: 081208ge STA: G.G.27<br />
TOP: Quadril<strong>at</strong>eral Proofs
23 ANS:<br />
32.<br />
16 x − 3<br />
=<br />
20 x + 5<br />
16x + 80 = 20x − 60<br />
140 = 4x<br />
35 = x<br />
. AC = x − 3 = 35 − 3 = 32<br />
PTS: 4 REF: 011137ge STA: G.G.46 TOP: Side Splitter Theorem<br />
24 ANS:<br />
PTS: 2 REF: 011133ge STA: G.G.17 TOP: Constructions<br />
25 ANS:<br />
A′(5,−4), B′(5,1), C ′(2,1), D′(2,−6); A″(5,4), B″(5,−1), C ″(2,−1), D″(2,6)<br />
PTS: 4<br />
KEY: grids<br />
REF: 061236ge STA: G.G.58 TOP: Compositions of Transform<strong>at</strong>ions<br />
26 ANS: 3<br />
<br />
180(n − 2) <br />
180(n − 2) = n 180 −<br />
n<br />
<br />
<br />
180n − 360 = 180n − 180n + 360<br />
180n = 720<br />
n = 4<br />
ID: A<br />
PTS: 2 REF: 081223ge STA: G.G.36 TOP: Interior and Exterior Angles of Polygons
27 ANS:<br />
2<br />
x + 2<br />
x<br />
= x + 6<br />
4<br />
x 2 + 6x = 4x + 8<br />
x 2 + 2x − 8 = 0<br />
(x + 4)(x − 2) = 0<br />
x = 2<br />
PTS: 4 REF: 081137ge STA: G.G.45 TOP: Similarity<br />
KEY: basic<br />
28 ANS: 4<br />
−3 + x<br />
−5 = . 2 =<br />
2<br />
−10 = −3 + x<br />
−7 = x<br />
6 + y<br />
2<br />
4 = 6 + y<br />
−2 = y<br />
ID: A<br />
PTS: 2 REF: 081203ge STA: G.G.66 TOP: Midpoint<br />
29 ANS: 3 PTS: 2 REF: 011104ge STA: G.G.38<br />
TOP: Parallelograms<br />
30 ANS: 2 PTS: 2 REF: 011125ge STA: G.G.74<br />
TOP: Graphing Circles<br />
31 ANS:<br />
∠B and ∠E are right angles because of the definition of perpendicular lines. ∠B ≅ ∠E because all right angles<br />
are congruent. ∠BFD and ∠DFE are supplementary and ∠ECA and ∠ACB are supplementary because of the<br />
definition of supplementary angles. ∠DFE ≅ ∠ACB because angles supplementary to congruent angles are<br />
congruent. ABC ∼ DEF because of AA.<br />
PTS: 4 REF: 011136ge STA: G.G.44 TOP: Similarity Proofs<br />
32 ANS:<br />
PTS: 2 REF: 011230ge STA: G.G.22 TOP: Locus<br />
33 ANS: 4 PTS: 2 REF: 081224ge STA: G.G.21<br />
TOP: Centroid, Orthocenter, Incenter and Circumcenter<br />
34 ANS: 2<br />
4x + 10<br />
= 2x + 5<br />
2<br />
PTS: 2 REF: 011103ge STA: G.G.42 TOP: Midsegments
35 ANS: 3 PTS: 2 REF: 061111ge STA: G.G.38<br />
TOP: Parallelograms<br />
36 ANS: 4<br />
y = mx + b<br />
3 = 3<br />
(−2) + b<br />
2<br />
3 = −3 + b<br />
6 = b<br />
PTS: 2 REF: 011114ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
37 ANS: 1 PTS: 2 REF: 061108ge STA: G.G.9<br />
TOP: Planes<br />
38 ANS: 2 PTS: 2 REF: 061202ge STA: G.G.24<br />
TOP: Neg<strong>at</strong>ions<br />
39 ANS: 3<br />
PTS: 2 REF: 011112ge STA: G.G.49 TOP: Chords<br />
40 ANS: 1<br />
40 − 24<br />
2<br />
= 8. 10 2 − 8 2 = 6.<br />
PTS: 2<br />
41 ANS: 1<br />
REF: 061204ge STA: G.G.40 TOP: Trapezoids<br />
−4 + x<br />
1 = .<br />
2<br />
3 + y<br />
5 = .<br />
2<br />
−4 + x = 2<br />
x = 6<br />
3 + y = 10<br />
y = 7<br />
PTS: 2 REF: 081115ge STA: G.G.66 TOP: Midpoint<br />
ID: A
42 ANS:<br />
PTS: 2<br />
43 ANS: 3<br />
REF: 061232ge STA: G.G.17 TOP: Constructions<br />
x + 2x + 15 = 5x + 15 2(5) + 15 = 25<br />
3x + 15 = 5x + 5<br />
10 = 2x<br />
5 = x<br />
PTS: 2 REF: 011127ge STA: G.G.32 TOP: Exterior Angle Theorem<br />
44 ANS:<br />
PTS: 4 REF: 061135ge STA: G.G.23 TOP: Locus<br />
45 ANS: 2<br />
The slope of x + 2y = 3 is m = −A<br />
B<br />
= −1<br />
2 . m ⊥<br />
= 2.<br />
PTS: 2<br />
46 ANS: 2<br />
REF: 081122ge STA: G.G.62 TOP: Parallel and Perpendicular Lines<br />
(n − 2)180 = (6 − 2)180 = 720. 720<br />
= 120.<br />
6<br />
ID: A<br />
PTS: 2<br />
47 ANS: 3<br />
3<br />
× 180 = 36<br />
8 + 3 + 4<br />
REF: 081125ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons<br />
PTS: 2 REF: 011210ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles
48 ANS:<br />
52, 40, 80. 360 − (56 + 112) = 192.<br />
192 − 112<br />
1<br />
× 192 = 48<br />
4<br />
56 + 48<br />
2<br />
= 52<br />
2<br />
= 40.<br />
112 + 48<br />
2<br />
PTS: 6 REF: 081238ge STA: G.G.51 TOP: Arcs Determined by Angles<br />
KEY: inscribed<br />
49 ANS:<br />
V = πr 2 h<br />
600π = πr 2 ⋅ 12<br />
50 = r 2<br />
25 2 = r<br />
5 2 = r<br />
. L = 2πrh = 2π ⋅ 5 2 ⋅ 12 ≈ 533.1<br />
= 80<br />
PTS: 4 REF: 011236ge STA: G.G.14 TOP: Volume<br />
50 ANS:<br />
No, ∠KGH is not congruent to ∠GKH .<br />
PTS: 2 REF: 081135ge STA: G.G.31 TOP: Isosceles Triangle Theorem<br />
51 ANS: 3 PTS: 2 REF: 081104ge STA: G.G.55<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
52 ANS: 3 PTS: 2 REF: 011209ge STA: G.G.44<br />
TOP: Similarity Proofs<br />
53 ANS: 2 PTS: 2 REF: 081108ge STA: G.G.54<br />
TOP: Reflections KEY: basic<br />
54 ANS:<br />
2 is not a prime number, false.<br />
PTS: 2 REF: 081229ge STA: G.G.24 TOP: Neg<strong>at</strong>ions<br />
55 ANS: 3 PTS: 2 REF: 081128ge STA: G.G.39<br />
TOP: Special Parallelograms<br />
ID: A
56 ANS:<br />
PTS: 2 REF: 081130ge STA: G.G.18 TOP: Constructions<br />
57 ANS: 2 PTS: 2 REF: 061121ge STA: G.G.22<br />
TOP: Locus<br />
58 ANS: 4<br />
PTS: 2 REF: 081114ge STA: G.G.28 TOP: Triangle Congruency<br />
59 ANS: 4<br />
Parallel lines intercept congruent arcs.<br />
PTS: 2<br />
60 ANS:<br />
REF: 081201ge STA: G.G.52 TOP: Chords<br />
(−4 − 2) 2 + (3 − 5) 2 = 36 + 4 = 40 = 4 10 = 2 10 .<br />
PTS: 2 REF: 081232ge STA: G.G.67 TOP: Distance<br />
61 ANS: 2 PTS: 2 REF: 011206ge STA: G.G.32<br />
TOP: Exterior Angle Theorem<br />
62 ANS: 1 PTS: 2 REF: 081113ge STA: G.G.54<br />
TOP: Reflections KEY: basic<br />
63 ANS: 2<br />
7 + (−3)<br />
M x = = 2. M Y =<br />
2<br />
−1 + 3<br />
2<br />
= 1.<br />
PTS: 2 REF: 011106ge STA: G.G.66 TOP: Midpoint<br />
64 ANS: 2 PTS: 2 REF: 081120ge STA: G.G.8<br />
TOP: Planes<br />
ID: A
65 ANS: 4 PTS: 2 REF: 011212ge STA: G.G.71<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
66 ANS: 1 PTS: 2 REF: 011120ge STA: G.G.18<br />
TOP: Constructions<br />
67 ANS: 1 PTS: 2 REF: 081116ge STA: G.G.7<br />
TOP: Planes<br />
68 ANS: 3 PTS: 2 REF: 061218ge STA: G.G.36<br />
TOP: Interior and Exterior Angles of Polygons<br />
69 ANS: 3 PTS: 2 REF: 061102ge STA: G.G.29<br />
TOP: Triangle Congruency<br />
70 ANS:<br />
180 − (90 + 63) = 27<br />
ID: A<br />
PTS: 2 REF: 061230ge STA: G.G.35 TOP: Parallel Lines and Transversals<br />
71 ANS: 4<br />
AB is a vertical line, so its perpendicular bisector is a horizontal line through the midpoint of AB, which is (0,3).<br />
PTS: 2 REF: 011225ge STA: G.G.68 TOP: Perpendicular Bisector<br />
72 ANS: 4<br />
6 2 = x(x + 5)<br />
36 = x 2 + 5x<br />
0 = x 2 + 5x − 36<br />
0 = (x + 9)(x − 4)<br />
x = 4<br />
PTS: 2 REF: 011123ge STA: G.G.47 TOP: Similarity<br />
KEY: leg<br />
73 ANS: 3 PTS: 2 REF: 081111ge STA: G.G.32<br />
TOP: Exterior Angle Theorem<br />
74 ANS: 4 PTS: 2 REF: 081101ge STA: G.G.25<br />
TOP: Compound St<strong>at</strong>ements KEY: conjunction<br />
75 ANS: 3<br />
(3,−2) → (2,3) → (8,12)<br />
PTS: 2 REF: 011126ge STA: G.G.54 TOP: Compositions of Transform<strong>at</strong>ions<br />
KEY: basic<br />
76 ANS: 3<br />
−5 + 3 = −2 2 + −4 = −2<br />
PTS: 2 REF: 011107ge STA: G.G.54 TOP: Transl<strong>at</strong>ions
77 ANS:<br />
<br />
(7,5) m AB =<br />
<br />
3 + 7<br />
2<br />
3 + 9 <br />
,<br />
2 <br />
= (5,6) m 7 + 11<br />
BC = ,<br />
2<br />
9 + 3<br />
<br />
<br />
2<br />
PTS: 2 REF: 081134ge STA: G.G.21<br />
TOP: Centroid, Orthocenter, Incenter and Circumcenter<br />
78 ANS:<br />
V = 4<br />
3 π ⋅ 93 = 972π<br />
<br />
= (9,6)<br />
<br />
PTS: 2 REF: 081131ge STA: G.G.16 TOP: Surface Area<br />
79 ANS:<br />
9.1. (11)(8)h = 800<br />
h ≈ 9.1<br />
PTS: 2<br />
80 ANS: 3<br />
180 − 70<br />
= 55<br />
2<br />
REF: 061131ge STA: G.G.12 TOP: Volume<br />
PTS: 2 REF: 061205ge STA: G.G.52 TOP: Chords<br />
81 ANS: 4<br />
6 2 − 2 2 = 32 = 16 2 = 4 2<br />
PTS: 2 REF: 081124ge STA: G.G.49 TOP: Chords<br />
82 ANS: 1 PTS: 2 REF: 011207ge STA: G.G.20<br />
TOP: Constructions<br />
83 ANS: 4<br />
m∠A = 80<br />
PTS: 2 REF: 011115ge STA: G.G.34 TOP: Angle Side Rel<strong>at</strong>ionship<br />
84 ANS: 3<br />
y = mx + b<br />
−1 = 2(2) + b<br />
−5 = b<br />
PTS: 2 REF: 011224ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
85 ANS: 1 PTS: 2 REF: 011122ge STA: G.G.28<br />
TOP: Triangle Congruency<br />
ID: A
86 ANS: 2 PTS: 2 REF: 081202ge STA: G.G.55<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
87 ANS: 2 PTS: 2 REF: 061101ge STA: G.G.18<br />
TOP: Constructions<br />
88 ANS: 3 PTS: 2 REF: 081218ge STA: G.G.1<br />
TOP: Planes<br />
89 ANS: 3 PTS: 2 REF: 061224ge STA: G.G.45<br />
TOP: Similarity KEY: basic<br />
90 ANS:<br />
Yes. A reflection is an isometry.<br />
PTS: 2 REF: 061132ge STA: G.G.56 TOP: Identifying Transform<strong>at</strong>ions<br />
91 ANS: 2 PTS: 2 REF: 011211ge STA: G.G.55<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
92 ANS: 2<br />
m = −A<br />
B<br />
= −4<br />
2<br />
= −2 y = mx + b<br />
2 = −2(2) + b<br />
6 = b<br />
PTS: 2 REF: 081112ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
93 ANS: 1<br />
PTS: 2 REF: 061211ge STA: G.G.31 TOP: Isosceles Triangle Theorem<br />
94 ANS:<br />
PTS: 2<br />
95 ANS:<br />
180 − 80<br />
= 50<br />
2<br />
REF: 011233ge STA: G.G.17 TOP: Constructions<br />
PTS: 2 REF: 081129ge STA: G.G.52 TOP: Chords<br />
ID: A
96 ANS: 2<br />
AC = BD<br />
AC − BC = BD − BC<br />
AB = CD<br />
PTS: 2 REF: 061206ge STA: G.G.27 TOP: Line Proofs<br />
97 ANS: 3 PTS: 2 REF: 011202ge STA: G.G.21<br />
TOP: Centroid, Orthocenter, Incenter and Circumcenter<br />
98 ANS: 4 PTS: 2 REF: 011124ge STA: G.G.51<br />
TOP: Arcs Determined by Angles KEY: inscribed<br />
99 ANS: 1<br />
m = 3<br />
2<br />
y = mx + b<br />
2 = 3<br />
(1) + b<br />
2<br />
1<br />
= b<br />
2<br />
ID: A<br />
PTS: 2 REF: 081217ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
100 ANS: 2 PTS: 2 REF: 081205ge STA: G.G.17<br />
TOP: Constructions<br />
101 ANS: 4 PTS: 2 REF: 061203ge STA: G.G.9<br />
TOP: Planes<br />
102 ANS: 3 PTS: 2 REF: 011217ge STA: G.G.64<br />
TOP: Parallel and Perpendicular Lines<br />
103 ANS: 1 PTS: 2 REF: 011218ge STA: G.G.3<br />
TOP: Planes<br />
104 ANS:<br />
OA ≅ OB because all radii are equal. OP ≅ OP because of the reflexive property. OA⊥ PA and OB⊥ PB<br />
because tangents to a circle are perpendicular to a radius <strong>at</strong> a point on a circle. ∠PAO and ∠PBO are right angles<br />
because of the definition of perpendicular. ∠PAO ≅ ∠PBO because all right angles are congruent.<br />
AOP ≅ BOP because of HL. ∠AOP ≅ ∠BOP because of CPCTC.<br />
PTS: 6 REF: 061138ge STA: G.G.27 TOP: Circle Proofs
105 ANS:<br />
A' (−2,1), B' (−3,−4), and C' (5,−3)<br />
PTS: 2 REF: 081230ge STA: G.G.54 TOP: Rot<strong>at</strong>ions<br />
106 ANS: 4 PTS: 2 REF: 061103ge STA: G.G.60<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
107 ANS: 3<br />
d = (−1 − 4) 2 + (0 − (−3)) 2 = 25 + 9 = 34<br />
PTS: 2 REF: 061217ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
108 ANS:<br />
PTS: 4 REF: 011135ge STA: G.G.23 TOP: Locus<br />
109 ANS: 2<br />
m = −A<br />
B<br />
= −20<br />
−2 = 10. m ⊥<br />
= − 1<br />
10<br />
PTS: 2 REF: 061219ge STA: G.G.62 TOP: Parallel and Perpendicular Lines<br />
110 ANS: 1 PTS: 2 REF: 061113ge STA: G.G.63<br />
TOP: Parallel and Perpendicular Lines<br />
111 ANS: 1 PTS: 2 REF: 011128ge STA: G.G.2<br />
TOP: Planes<br />
112 ANS: 3<br />
The slope of 9x − 3y = 27 is m = −A<br />
B<br />
−9<br />
= = 3, which is the opposite reciprocal of −1<br />
−3 3 .<br />
PTS: 2 REF: 081225ge STA: G.G.62 TOP: Parallel and Perpendicular Lines<br />
ID: A
113 ANS: 4<br />
The slope of 3x + 5y = 4 is m = −A<br />
B<br />
= −3<br />
5 . m ⊥<br />
= 5<br />
3 .<br />
PTS: 2 REF: 061127ge STA: G.G.62 TOP: Parallel and Perpendicular Lines<br />
114 ANS:<br />
R′(−3,−2), S' (−4,4), and T ′(2,2).<br />
PTS: 2 REF: 011232ge STA: G.G.54 TOP: Rot<strong>at</strong>ions<br />
115 ANS:<br />
3a + a − 6<br />
(2a − 3,3b + 2). ,<br />
2<br />
2b − 1 + 4b + 5<br />
<br />
<br />
4a − 6<br />
= ,<br />
<br />
2 2<br />
6b + 4<br />
<br />
<br />
= (2a − 3,3b + 2)<br />
2 <br />
PTS: 2 REF: 061134ge STA: G.G.66 TOP: Midpoint<br />
116 ANS:<br />
The slope of y = 2x + 3 is 2. The slope of 2y + x = 6 is −A<br />
B<br />
lines are perpendicular.<br />
ID: A<br />
−1<br />
= . Since the slopes are opposite reciprocals, the<br />
2<br />
PTS: 2 REF: 011231ge STA: G.G.63 TOP: Parallel and Perpendicular Lines<br />
117 ANS: 4 PTS: 2 REF: 081211ge STA: G.G.5<br />
TOP: Planes<br />
118 ANS: 4<br />
x 2 − 6x + 2x − 3 = 9x + 27<br />
x 2 − 4x − 3 = 9x + 27<br />
x 2 − 13x − 30 = 0<br />
(x − 15)(x + 2) = 0<br />
x = 15, − 2<br />
PTS: 2 REF: 061225ge STA: G.G.32 TOP: Exterior Angle Theorem<br />
119 ANS:<br />
<br />
M<br />
<br />
−7 + 5<br />
2<br />
, 2 + 4<br />
2<br />
<br />
<br />
3 + 5<br />
= M(−1,3). N<br />
<br />
2<br />
, −4 + 4<br />
2<br />
<br />
= N(4,0). MN is a midsegment.<br />
<br />
PTS: 4 REF: 011237ge STA: G.G.42 TOP: Midsegments<br />
120 ANS: 1 PTS: 2 REF: 061125ge STA: G.G.39<br />
TOP: Special Parallelograms
121 ANS: 1 PTS: 2 REF: 061104ge STA: G.G.43<br />
TOP: Centroid<br />
122 ANS: 1 PTS: 2 REF: 061110ge STA: G.G.72<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
123 ANS:<br />
(x − 5) 2 + (y + 4) 2 = 36<br />
PTS: 2 REF: 081132ge STA: G.G.72 TOP: Equ<strong>at</strong>ions of Circles<br />
124 ANS: 3<br />
8 2 + 24 2 ≠ 25 2<br />
PTS: 2 REF: 011111ge STA: G.G.48 TOP: Pythagorean Theorem<br />
125 ANS: 3 PTS: 2 REF: 081209ge STA: G.G.71<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
126 ANS: 3 PTS: 2 REF: 081204ge STA: G.G.59<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
127 ANS: 3<br />
PTS: 2 REF: 081118ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
128 ANS:<br />
G″(3,3),H ″(7,7),S ″(−1,9)<br />
PTS: 4 REF: 081136ge STA: G.G.58 TOP: Compositions of Transform<strong>at</strong>ions<br />
129 ANS: 2 PTS: 2 REF: 061208ge STA: G.G.19<br />
TOP: Constructions<br />
130 ANS: 1<br />
<br />
The diagonals of a parallelogram intersect <strong>at</strong> their midpoints. M AC<br />
<br />
<br />
1 + 3<br />
2<br />
, 5 + (−1)<br />
2<br />
<br />
= (2,2)<br />
<br />
ID: A<br />
PTS: 2 REF: 061209ge STA: G.G.69 TOP: Quadril<strong>at</strong>erals in the Coordin<strong>at</strong>e Plane
131 ANS: 1<br />
d = (4 − 1) 2 + (7 − 11) 2 = 9 + 16 = 25 = 5<br />
PTS: 2 REF: 011205ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
132 ANS: 4 PTS: 2 REF: 061114ge STA: G.G.73<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
133 ANS: 2<br />
The diagonals of a rhombus are perpendicular. 180 − (90 + 12) = 78<br />
PTS: 2 REF: 011204ge STA: G.G.39 TOP: Special Parallelograms<br />
134 ANS: 2<br />
5 − 3 = 2,5 + 3 = 8<br />
PTS: 2 REF: 011228ge STA: G.G.33 TOP: Triangle Inequality Theorem<br />
135 ANS: 3<br />
4x + 14 + 8x + 10 = 180<br />
12x = 156<br />
x = 13<br />
PTS: 2 REF: 081213ge STA: G.G.35 TOP: Parallel Lines and Transversals<br />
136 ANS: 4 PTS: 2 REF: 081216ge STA: G.G.45<br />
TOP: Similarity KEY: basic<br />
137 ANS: 1 PTS: 2 REF: 081121ge STA: G.G.39<br />
TOP: Special Parallelograms<br />
138 ANS:<br />
A′(7,−4),B′(7,−1). C ′(9,−4). The areas are equal because transl<strong>at</strong>ions preserve distance.<br />
PTS: 4 REF: 011235ge STA: G.G.55 TOP: Properties of Transform<strong>at</strong>ions<br />
139 ANS: 2 PTS: 2 REF: 081214ge STA: G.G.50<br />
TOP: Tangents KEY: point of tangency<br />
140 ANS: 3 PTS: 2 REF: 061210ge STA: G.G.71<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
141 ANS: 3 PTS: 2 REF: 081123ge STA: G.G.12<br />
TOP: Volume<br />
142 ANS: 4 PTS: 2 REF: 011118ge STA: G.G.25<br />
TOP: Compound St<strong>at</strong>ements KEY: general<br />
ID: A
143 ANS:<br />
EO = 6. CE = 10 2 − 6 2 = 8<br />
PTS: 2 REF: 011234ge STA: G.G.49 TOP: Chords<br />
144 ANS: 2 PTS: 2 REF: 081212ge STA: G.G.72<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
145 ANS: 2<br />
TOP: Locus<br />
146 ANS: 2<br />
PTS: 2 REF: 081117ge STA: G.G.23<br />
V = 4<br />
3 π r 3 = 4<br />
3<br />
<br />
15 <br />
π ⋅<br />
2 <br />
3<br />
≈ 1767.1<br />
PTS: 2 REF: 061207ge STA: G.G.16 TOP: Volume and Surface Area<br />
147 ANS: 4<br />
The centroid divides each median into segments whose lengths are in the r<strong>at</strong>io 2 : 1.<br />
PTS: 2 REF: 081220ge STA: G.G.43 TOP: Centroid<br />
148 ANS: 3<br />
7x<br />
4<br />
= 7<br />
x<br />
7x 2 = 28<br />
x = 2<br />
. 7(2) = 14<br />
PTS: 2 REF: 061120ge STA: G.G.45 TOP: Similarity<br />
KEY: basic<br />
149 ANS: 4 PTS: 2 REF: 011108ge STA: G.G.27<br />
TOP: Angle Proofs<br />
150 ANS:<br />
m = −A<br />
B<br />
= 6<br />
2 = 3. m ⊥<br />
= −1<br />
3 .<br />
PTS: 2 REF: 011134ge STA: G.G.62 TOP: Parallel and Perpendicular Lines<br />
151 ANS: 2<br />
V = πr 2 h = π ⋅ 6 2 ⋅ 15 = 540π<br />
PTS: 2<br />
152 ANS: 3<br />
REF: 011117ge STA: G.G.14 TOP: Volume<br />
x 2 + 7 2 = (x + 1) 2<br />
x + 1 = 25<br />
x 2 + 49 = x 2 + 2x + 1<br />
48 = 2x<br />
24 = x<br />
PTS: 2 REF: 081127ge STA: G.G.48 TOP: Pythagorean Theorem<br />
ID: A
153 ANS: 1 PTS: 2 REF: 011102ge STA: G.G.55<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
154 ANS: 4<br />
TOP: Planes<br />
155 ANS: 2<br />
PTS: 2 REF: 061213ge STA: G.G.5<br />
V = 4<br />
3 π r 3 = 4<br />
3 π ⋅ 33 = 36π<br />
PTS: 2 REF: 061112ge STA: G.G.16 TOP: Volume and Surface Area<br />
156 ANS: 1<br />
AB = CD<br />
AB + BC = CD + BC<br />
AC = BD<br />
PTS: 2 REF: 081207ge STA: G.G.27 TOP: Line Proofs<br />
157 ANS:<br />
T ′(−6,3), A′(−3,3),P ′(−3,−1)<br />
PTS: 2 REF: 061229ge STA: G.G.54 TOP: Transl<strong>at</strong>ions<br />
158 ANS: 3<br />
bisect each other.<br />
ID: A<br />
. Opposite sides of a parallelogram are congruent and the diagonals of a parallelogram<br />
PTS: 2 REF: 061222ge STA: G.G.28 TOP: Triangle Congruency<br />
159 ANS:<br />
∠ACB ≅ ∠AED is given. ∠A ≅ ∠A because of the reflexive property. Therefore ABC ∼ ADE because of<br />
AA.<br />
PTS: 2 REF: 081133ge STA: G.G.44 TOP: Similarity Proofs<br />
160 ANS: 3 PTS: 2 REF: 061228ge STA: G.G.39<br />
TOP: Special Parallelograms
161 ANS: 3<br />
8<br />
2<br />
= 12<br />
x<br />
8x = 24<br />
x = 3<br />
.<br />
PTS: 2 REF: 061216ge STA: G.G.46 TOP: Side Splitter Theorem<br />
162 ANS: 1<br />
Parallel lines intercept congruent arcs.<br />
PTS: 2 REF: 061105ge STA: G.G.52 TOP: Chords<br />
163 ANS: 3 PTS: 2 REF: 081227ge STA: G.G.42<br />
TOP: Midsegments<br />
164 ANS:<br />
11. x 2 + 6x = x + 14.<br />
6(2) − 1 = 11<br />
x 2 + 5x − 14 = 0<br />
(x + 7)(x − 2) = 0<br />
x = 2<br />
PTS: 2<br />
165 ANS: 4<br />
REF: 081235ge STA: G.G.38 TOP: Parallelograms<br />
25 2 2 <br />
26 − 12 <br />
−<br />
<br />
2<br />
<br />
= 24<br />
ID: A<br />
PTS: 2 REF: 011219ge STA: G.G.40 TOP: Trapezoids<br />
166 ANS: 2<br />
TOP: Planes<br />
PTS: 2 REF: 011109ge STA: G.G.9<br />
167 ANS:<br />
−6 + 2<br />
m AB = ,<br />
2<br />
−2 + 8<br />
<br />
<br />
2 <br />
= D(2,3) m <br />
2 + 6 8 + −2 <br />
BC = , = E(4,3) F(0,−2). To prove th<strong>at</strong> ADEF is a<br />
2 2 <br />
parallelogram, show th<strong>at</strong> both pairs of opposite sides of the parallelogram are parallel by showing the opposite<br />
3 − −2 5<br />
sides have the same slope: m AD = = AF DE because all horizontal lines have the same slope. ADEF<br />
−2 − −6 4<br />
3 − −2 5<br />
mFE = =<br />
4 − 0 4<br />
is not a rhombus because not all sides are congruent. AD = 5 2 + 4 2 = 41 AF = 6<br />
PTS: 6 REF: 081138ge STA: G.G.69 TOP: Quadril<strong>at</strong>erals in the Coordin<strong>at</strong>e Plane
168 ANS: 2 PTS: 2 REF: 011203ge STA: G.G.73<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
169 ANS: 4<br />
5<br />
× 180 = 90<br />
2 + 3 + 5<br />
ID: A<br />
PTS: 2 REF: 081119ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles<br />
170 ANS: 2 PTS: 2 REF: 061107ge STA: G.G.32<br />
TOP: Exterior Angle Theorem<br />
171 ANS: 4 PTS: 2 REF: 011216ge STA: G.G.29<br />
TOP: Triangle Congruency<br />
172 ANS: 2 PTS: 2 REF: 061227ge STA: G.G.56<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
173 ANS: 2<br />
17 2 − 15 2 = 8. 17 − 8 = 9<br />
PTS: 2<br />
174 ANS: 4<br />
REF: 061221ge STA: G.G.49 TOP: Chords<br />
x ⋅ 4x = 6 2<br />
. PQ = 4x + x = 5x = 5(3) = 15<br />
4x 2 = 36<br />
x = 3<br />
PTS: 2 REF: 011227ge STA: G.G.47 TOP: Similarity<br />
KEY: leg<br />
175 ANS:<br />
30. 3x + 4x + 5x = 360.<br />
mLN : mNK :mKL = 90:120:150.<br />
x = 20<br />
150 − 90<br />
2<br />
PTS: 4 REF: 061136ge STA: G.G.51 TOP: Arcs Determined by Angles<br />
KEY: outside circle<br />
176 ANS: 2<br />
d = (−1 − 7) 2 + (9 − 4) 2 = 64 + 25 = 89<br />
= 30<br />
PTS: 2 REF: 061109ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
177 ANS: 2 PTS: 2 REF: 081226ge STA: G.G.69<br />
TOP: Triangles in the Coordin<strong>at</strong>e Plane<br />
178 ANS: 1 PTS: 2 REF: 011221ge STA: G.G.10<br />
TOP: Solids
179 ANS:<br />
2x − 20 = x + 20.<br />
mAB = x + 20 = 40 + 20 = 60<br />
x = 40<br />
PTS: 2<br />
180 ANS: 1<br />
REF: 011229ge STA: G.G.52 TOP: Chords<br />
7x + 4 = 2(2x + 5) . PM = 2(2) + 5 = 9<br />
7x + 4 = 4x + 10<br />
3x = 6<br />
x = 2<br />
PTS: 2 REF: 011226ge STA: G.G.43 TOP: Centroid<br />
181 ANS: 1<br />
The length of the midsegment of a trapezoid is the average of the lengths of its bases.<br />
x + 3 + 5x − 9<br />
2<br />
ID: A<br />
= 2x + 2.<br />
6x − 6 = 4x + 4<br />
2x = 10<br />
PTS: 2 REF: 081221ge STA: G.G.40 TOP: Trapezoids<br />
182 ANS:<br />
∠B and ∠C are right angles because perpendicular lines form right angles. ∠B ≅ ∠C because all right<br />
angles are congruent. ∠AEB ≅ ∠DEC because vertical angles are congruent. ABE ≅ DCE because of<br />
ASA. AB ≅ DC because CPCTC.<br />
PTS: 4 REF: 061235ge STA: G.G.27 TOP: Triangle Proofs<br />
183 ANS: 4<br />
20 + 8 + 10 + 6 = 44.<br />
PTS: 2 REF: 061211ge STA: G.G.42 TOP: Midsegments<br />
x = 5
184 ANS:<br />
PTS: 2 REF: 061234ge STA: G.G.23 TOP: Locus<br />
185 ANS: 1<br />
PTS: 2 REF: 081219ge STA: G.G.34 TOP: Angle Side Rel<strong>at</strong>ionship<br />
186 ANS: 2<br />
3x + x + 20 + x + 20 = 180<br />
5x = 40<br />
x = 28<br />
PTS: 2 REF: 081222ge STA: G.G.31 TOP: Isosceles Triangle Theorem<br />
187 ANS: 4 PTS: 2 REF: 061118ge STA: G.G.1<br />
TOP: Planes<br />
188 ANS: 3<br />
d = (1 − 9) 2 + (−4 − 2) 2 = 64 + 36 = 100 = 10<br />
PTS: 2 REF: 081107ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
189 ANS:<br />
The medians of a triangle are not concurrent. False.<br />
PTS: 2 REF: 061129ge STA: G.G.24 TOP: Neg<strong>at</strong>ions<br />
190 ANS: 1 PTS: 2 REF: 011112ge STA: G.G.39<br />
TOP: Special Parallelograms<br />
191 ANS: 3<br />
The slope of 2y = x + 2 is 1<br />
, which is the opposite reciprocal of −2. 3 = −2(4) + b<br />
2<br />
11 = b<br />
PTS: 2 REF: 081228ge STA: G.G.64 TOP: Parallel and Perpendicular Lines<br />
ID: A
192 ANS:<br />
The slope of x + 2y = 4 is m = −A −1<br />
−A 2<br />
= . The slope of 4y − 2x = 12 is =<br />
B 2 B 4<br />
equal nor opposite reciprocals, the lines are neither parallel nor perpendicular.<br />
ID: A<br />
1<br />
= . Since the slopes are neither<br />
2<br />
PTS: 2 REF: 061231ge STA: G.G.63 TOP: Parallel and Perpendicular Lines<br />
193 ANS: 4<br />
m = −A<br />
B<br />
−3<br />
= . y = mx + b<br />
2<br />
−1 = −3 <br />
<br />
(2) + b<br />
2 <br />
−1 = −3 + b<br />
2 = b<br />
PTS: 2<br />
194 ANS: 4<br />
REF: 061226ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
25 2 − 7 2 = 24<br />
PTS: 2 REF: 081105ge STA: G.G.50 TOP: Tangents<br />
KEY: point of tangency<br />
195 ANS: 3<br />
5 2 + 12 2 = 13<br />
PTS: 2<br />
196 ANS: 2<br />
50 + x<br />
= 34<br />
2<br />
50 + x = 68<br />
x = 18<br />
REF: 061116ge STA: G.G.39 TOP: Special Parallelograms<br />
PTS: 2<br />
KEY: inside circle<br />
REF: 011214ge STA: G.G.51 TOP: Arcs Determined by Angles<br />
197 ANS: 1 PTS: 2 REF: 061223ge STA: G.G.73<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
198 ANS: 4 PTS: 2 REF: 011222ge STA: G.G.34<br />
TOP: Angle Side Rel<strong>at</strong>ionship<br />
199 ANS: 2<br />
6x + 42 = 18x − 12<br />
54 = 12x<br />
x = 54<br />
= 4.5<br />
12<br />
PTS: 2 REF: 011201ge STA: G.G.35 TOP: Parallel Lines and Transversals
200 ANS:<br />
PTS: 4 REF: 081236ge STA: G.G.58 TOP: Compositions of Transform<strong>at</strong>ions<br />
KEY: grids<br />
201 ANS:<br />
ID: A<br />
The length of each side of quadril<strong>at</strong>eral is 5. Since each side is congruent, quadril<strong>at</strong>eral<br />
MATH is a rhombus. The slope of MH is 0 and the slope of HT is − 4<br />
. Since the slopes are not neg<strong>at</strong>ive<br />
3<br />
reciprocals, the sides are not perpendicular and do not form rights angles. Since adjacent sides are not<br />
perpendicular, quadril<strong>at</strong>eral MATH is not a square.<br />
PTS: 6 REF: 011138ge STA: G.G.69 TOP: Quadril<strong>at</strong>erals in the Coordin<strong>at</strong>e Plane<br />
202 ANS: 4<br />
4(x + 4) = 8 2<br />
4x + 16 = 64<br />
4x = 48<br />
x = 12<br />
PTS: 2 REF: 061117ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: tangent and secant
203 ANS: 1<br />
x 2 = 7(16 − 7)<br />
x 2 = 63<br />
x = 9 7<br />
x = 3 7<br />
PTS: 2 REF: 061128ge STA: G.G.47 TOP: Similarity<br />
KEY: altitude<br />
204 ANS: 2 PTS: 2 REF: 061201ge STA: G.G.59<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
205 ANS:<br />
x 2 = 9 ⋅ 8<br />
x = 72<br />
x = 36 2<br />
x = 6 2<br />
PTS: 2 REF: 011132ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: two chords<br />
206 ANS: 1 PTS: 2 REF: 011220ge STA: G.G.72<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
207 ANS: 4 PTS: 2 REF: 011208ge STA: G.G.53<br />
TOP: Segments Intercepted by Circle KEY: two tangents<br />
208 ANS: 4 PTS: 2 REF: 081206ge STA: G.G.30<br />
TOP: Interior and Exterior Angles of Triangles<br />
209 ANS: 3 PTS: 2 REF: 011116ge STA: G.G.71<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
210 ANS: 1<br />
PTS: 2 REF: 081210ge STA: G.G.28 TOP: Triangle Congruency<br />
211 ANS: 4 PTS: 2 REF: 061124ge STA: G.G.31<br />
TOP: Isosceles Triangle Theorem<br />
ID: A
212 ANS: 3<br />
5 10<br />
=<br />
7 x<br />
5x = 70<br />
x = 14<br />
PTS: 2<br />
213 ANS: 4<br />
REF: 081103ge STA: G.G.46 TOP: Side Splitter Theorem<br />
x + 6y = 12<br />
3(x − 2) = −y − 4<br />
6y = −x + 12<br />
y = − 1<br />
x + 2<br />
6<br />
m = − 1<br />
6<br />
−3(x − 2) = y + 4<br />
m = −3<br />
PTS: 2 REF: 011119ge STA: G.G.63 TOP: Parallel and Perpendicular Lines<br />
214 ANS: 4 PTS: 2 REF: 081110ge STA: G.G.71<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
215 ANS:<br />
PTS: 6 REF: 061238ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
216 ANS: 3<br />
PTS: 2 REF: 011101ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: two tangents<br />
217 ANS: 3 PTS: 2 REF: 011110ge STA: G.G.21<br />
KEY: Centroid, Orthocenter, Incenter and Circumcenter<br />
ID: A
218 ANS: 3<br />
7x = 5x + 30<br />
2x = 30<br />
x = 15<br />
PTS: 2 REF: 081109ge STA: G.G.35 TOP: Parallel Lines and Transversals<br />
219 ANS:<br />
PTS: 4 REF: 081237ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
220 ANS: 2 PTS: 2 REF: 061115ge STA: G.G.69<br />
TOP: Triangles in the Coordin<strong>at</strong>e Plane<br />
221 ANS: 2<br />
V = 4<br />
3 π r 3 = 4<br />
3<br />
<br />
6 <br />
π ⋅<br />
2 <br />
3<br />
≈ 36π<br />
PTS: 2 REF: 081215ge STA: G.G.16 TOP: Volume and Surface Area<br />
222 ANS: 3<br />
ID: A<br />
PTS: 2 REF: 011223ge STA: G.G.36 TOP: Interior and Exterior Angles of Polygons<br />
223 ANS:<br />
PTS: 2 REF: 081234ge STA: G.G.23 TOP: Locus<br />
224 ANS:<br />
V = πr 2 h = π(5) 2 ⋅ 7 = 175π<br />
PTS: 2 REF: 081231ge STA: G.G.14 TOP: Volume<br />
225 ANS: 2 PTS: 2 REF: 061126ge STA: G.G.59<br />
TOP: Properties of Transform<strong>at</strong>ions
226 ANS:<br />
x(x + 2) = 12 ⋅ 2.<br />
RT = 6 + 4 = 10. y ⋅ y = 18 ⋅ 8<br />
x 2 + 2x − 24 = 0<br />
(x + 6)(x − 4) = 0<br />
x = 4<br />
y 2 = 144<br />
y = 12<br />
PTS: 4 REF: 061237ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: tangent and secant<br />
ID: A
<strong>Geometry</strong> <strong>Regents</strong> <strong>at</strong> <strong>Random</strong> <strong>Worksheets</strong><br />
Answer Section<br />
227 ANS:<br />
18. If the r<strong>at</strong>io of TA to AC is 1:3, the r<strong>at</strong>io of TE to ES is also 1:3. x + 3x = 24.<br />
3(6) = 18.<br />
x = 6<br />
PTS: 4 REF: 060935ge STA: G.G.50 TOP: Tangents<br />
KEY: common tangency<br />
228 ANS: 1<br />
x + 2x + 2 + 3x + 4 = 180<br />
6x + 6 = 180<br />
x = 29<br />
ID: A<br />
PTS: 2 REF: 011002ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles<br />
229 ANS: 4 PTS: 2 REF: 011012ge STA: G.G.1<br />
TOP: Planes<br />
230 ANS: 2<br />
∠ACB and ∠ECD are congruent vertical angles and ∠CAB ≅ ∠CED.<br />
PTS: 2 REF: 060917ge STA: G.G.44 TOP: Similarity Proofs
231 ANS:<br />
ID: A<br />
PTS: 4 REF: 011037ge STA: G.G.23 TOP: Locus<br />
232 ANS:<br />
Contrapositive-If two angles of a triangle are not congruent, the sides opposite those angles are not congruent.<br />
PTS: 2 REF: fall0834ge STA: G.G.26 TOP: Conditional St<strong>at</strong>ements<br />
233 ANS: 2<br />
The slope of y = 1<br />
2<br />
1<br />
x + 5 is . The slope of a perpendicular line is −2. y = mx + b .<br />
2<br />
5 = (−2)(−2) + b<br />
PTS: 2 REF: 060907ge STA: G.G.64 TOP: Parallel and Perpendicular Lines<br />
234 ANS: 4<br />
TOP: Solids<br />
235 ANS: 2<br />
PTS: 2 REF: 060904ge STA: G.G.13<br />
The slope of a line in standard form is − A<br />
−2<br />
, so the slope of this line is = 2. A parallel line would also have a<br />
B −1<br />
slope of 2. Since the answers are in slope intercept form, find the y-intercept: y = mx + b<br />
−11 = 2(−3) + b<br />
−5 = b<br />
PTS: 2<br />
236 ANS:<br />
180 − 46<br />
67. = 67<br />
2<br />
REF: fall0812ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
PTS: 2 REF: 011029ge STA: G.G.31 TOP: Isosceles Triangle Theorem<br />
237 ANS: 4<br />
b = 1<br />
PTS: 2 REF: 081001ge STA: G.G.29 TOP: Triangle Congruency
238 ANS:<br />
y = −2x + 14. The slope of 2x + y = 3 is −A<br />
B<br />
= −2<br />
1<br />
= −2. y = mx + b<br />
4 = (−2)(5) + b<br />
b = 14<br />
PTS: 2<br />
239 ANS: 3<br />
36 + 20<br />
= 28<br />
2<br />
REF: 060931ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
PTS: 2 REF: 061019ge STA: G.G.51 TOP: Arcs Determined by Angles<br />
KEY: inside circle<br />
240 ANS:<br />
PTS: 2 REF: 081033ge STA: G.G.22 TOP: Locus<br />
241 ANS: 2 PTS: 2 REF: 060910ge STA: G.G.71<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
242 ANS: 3 PTS: 2 REF: fall0814ge STA: G.G.73<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
243 ANS: 4<br />
(n − 2)180 = (8 − 2)180 = 1080. 1080<br />
= 135.<br />
8<br />
.<br />
ID: A<br />
PTS: 2<br />
244 ANS: 2<br />
REF: fall0827ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons<br />
3x + 5 + x − 1<br />
M x = =<br />
2<br />
4x + 4<br />
3y + (−y)<br />
= 2x + 2. M Y = =<br />
2<br />
2<br />
2y<br />
= y.<br />
2<br />
PTS: 2 REF: 081019ge STA: G.G.66 TOP: Midpoint<br />
KEY: general
245 ANS:<br />
ID: A<br />
PTS: 2 REF: fall0830ge STA: G.G.55 TOP: Properties of Transform<strong>at</strong>ions<br />
246 ANS:<br />
AC ≅ EC and DC ≅ BC because of the definition of midpoint. ∠ACB ≅ ∠ECD because of vertical angles.<br />
ABC ≅ EDC because of SAS. ∠CDE ≅ ∠CBA because of CPCTC. BD is a transversal intersecting AB and<br />
ED. Therefore AB DE because ∠CDE and ∠CBA are congruent altern<strong>at</strong>e interior angles.<br />
PTS: 6 REF: 060938ge STA: G.G.27 TOP: Triangle Proofs<br />
247 ANS: 2<br />
PTS: 2 REF: 081007ge STA: G.G.28 TOP: Triangle Congruency<br />
248 ANS: 3<br />
(x + 3) 2 − 4 = 2x + 5<br />
x 2 + 6x + 9 − 4 = 2x + 5<br />
x 2 + 4x = 0<br />
x(x + 4) = 0<br />
x = 0,−4<br />
PTS: 2 REF: 081004ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
249 ANS: 2 PTS: 2 REF: 011003ge STA: G.G.55<br />
TOP: Properties of Transform<strong>at</strong>ions
250 ANS: 4 PTS: 2 REF: 061015ge STA: G.G.56<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
251 ANS:<br />
36, because a dil<strong>at</strong>ion does not affect angle measure. 10, because a dil<strong>at</strong>ion does affect distance.<br />
PTS: 4 REF: 011035ge STA: G.G.59 TOP: Properties of Transform<strong>at</strong>ions<br />
252 ANS:<br />
A″(8,2), B″(2,0), C ″(6,−8)<br />
PTS: 4 REF: 081036ge STA: G.G.58 TOP: Compositions of Transform<strong>at</strong>ions<br />
253 ANS: 4 PTS: 2 REF: 080915ge STA: G.G.56<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
254 ANS:<br />
y = 4<br />
3 x − 6. M −1 + 7<br />
x = = 3<br />
2<br />
M y =<br />
m =<br />
y − y M = m(x − x M ) .<br />
y − 1 = 4<br />
(x − 2)<br />
3<br />
1 + (−5)<br />
2<br />
1 − (−5)<br />
−1 − 7<br />
= −2<br />
= −3<br />
4<br />
The perpendicular bisector goes through (3,−2) and has a slope of 4<br />
3 .<br />
PTS: 4 REF: 080935ge STA: G.G.68 TOP: Perpendicular Bisector<br />
255 ANS:<br />
37. Since DE is a midsegment, AC = 14. 10 + 13 + 14 = 37<br />
PTS: 2 REF: 061030ge STA: G.G.42 TOP: Midsegments<br />
ID: A
256 ANS:<br />
34. 2x − 12 + x + 90 = 180<br />
3x + 78 = 90<br />
3x = 102<br />
x = 34<br />
ID: A<br />
PTS: 2 REF: 061031ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles<br />
257 ANS:<br />
True. The first st<strong>at</strong>ement is true and the second st<strong>at</strong>ement is false. In a disjunction, if either st<strong>at</strong>ement is true, the<br />
disjunction is true.<br />
PTS: 2<br />
KEY: disjunction<br />
258 ANS: 2<br />
REF: 060933ge STA: G.G.25 TOP: Compound St<strong>at</strong>ements<br />
140 − RS<br />
2<br />
= 40<br />
140 − RS = 80<br />
RS = 60<br />
PTS: 2 REF: 081025ge STA: G.G.51 TOP: Arcs Determined by Angles<br />
KEY: outside circle<br />
259 ANS: 4<br />
The slope of y = − 2<br />
3<br />
x − 5 is −2 . Perpendicular lines have slope th<strong>at</strong> are opposite reciprocals.<br />
3<br />
PTS: 2 REF: 080917ge STA: G.G.62 TOP: Parallel and Perpendicular Lines<br />
260 ANS:<br />
PTS: 4 REF: fall0835ge STA: G.G.42 TOP: Midsegments
261 ANS: 4<br />
Let AD = x. 36x = 12 2<br />
x = 4<br />
PTS: 2<br />
KEY: leg<br />
REF: 080922ge STA: G.G.47 TOP: Similarity<br />
262 ANS: 4 PTS: 2 REF: 080925ge STA: G.G.21<br />
TOP: Centroid, Orthocenter, Incenter and Circumcenter<br />
263 ANS: 2<br />
Parallel chords intercept congruent arcs. mAD = mBC = 60. m∠CDB = 1<br />
mBC = 30.<br />
2<br />
ID: A<br />
PTS: 2 REF: 060906ge STA: G.G.52 TOP: Chords<br />
264 ANS: 3<br />
Because OC is a radius, its length is 5. Since CE = 2 OE = 3. EDO is a 3-4-5 triangle. If ED = 4, BD = 8.<br />
PTS: 2 REF: fall0811ge STA: G.G.49 TOP: Chords<br />
265 ANS: 1<br />
Parallel lines intercept congruent arcs.<br />
PTS: 2 REF: 061001ge STA: G.G.52 TOP: Chords<br />
266 ANS: 4 PTS: 2 REF: 060912ge STA: G.G.23<br />
TOP: Locus<br />
267 ANS: 4 PTS: 2 REF: 080914ge STA: G.G.7<br />
TOP: Planes<br />
268 ANS: 3 PTS: 2 REF: 011028ge STA: G.G.26<br />
TOP: Conditional St<strong>at</strong>ements<br />
269 ANS: 3<br />
PTS: 2 REF: 080920ge STA: G.G.42 TOP: Midsegments<br />
270 ANS: 4 PTS: 2 REF: 011009ge STA: G.G.19<br />
TOP: Constructions<br />
271 ANS:<br />
2.4. 5a = 4 2<br />
5b = 3<br />
a = 3.2<br />
2<br />
h<br />
b = 1.8<br />
2 = ab<br />
h 2 = 3.2 ⋅ 1.8<br />
h = 5.76 = 2.4<br />
PTS: 4 REF: 081037ge STA: G.G.47 TOP: Similarity<br />
KEY: altitude
272 ANS:<br />
PTS: 4 REF: 080936ge STA: G.G.23 TOP: Locus<br />
273 ANS:<br />
PTS: 2 REF: 011032ge STA: G.G.20 TOP: Constructions<br />
274 ANS: 1 PTS: 2 REF: 080918ge STA: G.G.41<br />
TOP: Special Quadril<strong>at</strong>erals<br />
275 ANS: 2<br />
87 + 35<br />
2<br />
= 122<br />
2<br />
= 61<br />
PTS: 2 REF: 011015ge STA: G.G.51 TOP: Arcs Determined by Angles<br />
KEY: inside circle<br />
276 ANS: 3 PTS: 2 REF: fall0816ge STA: G.G.1<br />
TOP: Planes<br />
277 ANS: 3 PTS: 2 REF: 011007ge STA: G.G.31<br />
TOP: Isosceles Triangle Theorem<br />
278 ANS: 1<br />
V = πr 2 h<br />
1000 = πr 2 ⋅ 8<br />
r 2 = 1000<br />
8π<br />
r ≈ 6.3<br />
PTS: 2 REF: 080926ge STA: G.G.14 TOP: Volume<br />
279 ANS: 4 PTS: 2 REF: 061003ge STA: G.G.10<br />
TOP: Solids<br />
ID: A
280 ANS:<br />
70. 3x + 5 + 3x + 5 + 2x + 2x = 180<br />
10x + 10 = 360<br />
10x = 350<br />
x = 35<br />
2x = 70<br />
PTS: 2 REF: 081029ge STA: G.G.40 TOP: Trapezoids<br />
281 ANS:<br />
15 + 5 5.<br />
PTS: 4 REF: 060936ge STA: G.G.69 TOP: Triangles in the Coordin<strong>at</strong>e Plane<br />
282 ANS: 3 PTS: 2 REF: 081026ge STA: G.G.26<br />
TOP: Contrapositive<br />
283 ANS: 2<br />
PTS: 2 REF: 061026GE STA: G.G.51 TOP: Arcs Determined by Angles<br />
KEY: inscribed<br />
284 ANS: 4<br />
Median BF bisects AC so th<strong>at</strong> CF ≅ FA.<br />
PTS: 2 REF: fall0810ge STA: G.G.24 TOP: St<strong>at</strong>ements<br />
ID: A
285 ANS:<br />
8x − 5 = 3x + 30.<br />
4z − 8 = 3z.<br />
9y + 8 + 5y − 2 = 90.<br />
5x = 35<br />
x = 7<br />
z = 8<br />
14y + 6 = 90<br />
14y = 84<br />
y = 6<br />
PTS: 6 REF: 061038ge STA: G.G.39 TOP: Special Parallelograms<br />
286 ANS: 2 PTS: 2 REF: 011004ge STA: G.G.17<br />
TOP: Constructions<br />
287 ANS: 2 PTS: 2 REF: fall0806ge STA: G.G.9<br />
TOP: Planes<br />
288 ANS:<br />
y = 2<br />
A −2<br />
x − 9. The slope of 2x − 3y = 11 is − =<br />
3 B −3<br />
= 2<br />
3<br />
<br />
2 <br />
. −5 = (6) + b<br />
3 <br />
−5 = 4 + b<br />
b = −9<br />
PTS: 2 REF: 080931ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
289 ANS:<br />
4. l 1 w 1 h 1 = l 2 w 2 h 2<br />
10 × 2 × h = 5 × w 2 × h<br />
20 = 5w 2<br />
w 2 = 4<br />
PTS: 2 REF: 011030ge STA: G.G.11 TOP: Volume<br />
290 ANS: 2 PTS: 2 REF: 080927ge STA: G.G.4<br />
TOP: Planes<br />
ID: A
291 ANS:<br />
PTS: 2 REF: 061032ge STA: G.G.54 TOP: Reflections<br />
KEY: grids<br />
292 ANS:<br />
375π L = π r l = π(15)(25) = 375π<br />
PTS: 2 REF: 081030ge STA: G.G.15 TOP: L<strong>at</strong>eral Area<br />
293 ANS: 1<br />
y = x 2 − 4x = (4) 2 − 4(4) = 0. (4,0) is the only intersection.<br />
PTS: 2 REF: 060923ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
294 ANS:<br />
ID: A<br />
Because AB DC , AD ≅ BC since parallel chords intersect congruent arcs. ∠BDC ≅ ∠ACD because inscribed<br />
angles th<strong>at</strong> intercept congruent arcs are congruent. AD ≅ BC since congruent chords intersect congruent arcs.<br />
DC ≅ CD because of the reflexive property. Therefore, ACD ≅ BDC because of SAS.<br />
PTS: 6 REF: fall0838ge STA: G.G.27 TOP: Circle Proofs<br />
295 ANS:<br />
452. SA = 4πr 2 = 4π ⋅ 6 2 = 144π ≈ 452<br />
PTS: 2 REF: 061029ge STA: G.G.16 TOP: Surface Area<br />
296 ANS: 1 PTS: 2 REF: 011024ge STA: G.G.3<br />
TOP: Planes
297 ANS:<br />
110. 6x + 20 = x + 40 + 4x − 5<br />
6x + 20 = 5x + 35<br />
x = 15<br />
6((15) + 20 = 110<br />
ID: A<br />
PTS: 2<br />
298 ANS:<br />
REF: 081031ge STA: G.G.32 TOP: Exterior Angle Theorem<br />
Yes, m∠ABD = m∠BDC = 44 180 − (93 + 43) = 44 x + 19 + 2x + 6 + 3x + 5 = 180.<br />
Because altern<strong>at</strong>e interior<br />
angles ∠ABD and ∠CDB are congruent, AB is parallel to DC .<br />
6x + 30 = 180<br />
6x = 150<br />
x = 25<br />
x + 19 = 44<br />
PTS: 4<br />
299 ANS: 1<br />
REF: 081035ge STA: G.G.35 TOP: Parallel Lines and Transversals<br />
Opposite sides of a parallelogram are congruent. 4x − 3 = x + 3.<br />
SV = (2) + 3 = 5.<br />
3x = 6<br />
x = 2<br />
PTS: 2 REF: 011013ge STA: G.G.38 TOP: Parallelograms<br />
300 ANS: 4<br />
x 2 = (4 + 5) × 4<br />
x 2 = 36<br />
x = 6<br />
PTS: 2 REF: 011008ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: tangent and secant
301 ANS:<br />
PTS: 4 REF: 060937ge STA: G.G.54 TOP: Compositions of Transform<strong>at</strong>ions<br />
KEY: grids<br />
302 ANS: 1 PTS: 2 REF: 080911ge STA: G.G.73<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
303 ANS: 4<br />
180 − (50 + 30) = 100<br />
PTS: 2 REF: 081006ge STA: G.G.45 TOP: Similarity<br />
KEY: basic<br />
304 ANS: 4<br />
Corresponding angles of similar triangles are congruent.<br />
PTS: 2 REF: fall0826ge STA: G.G.45 TOP: Similarity<br />
KEY: perimeter and area<br />
305 ANS: 2<br />
Adjacent sides of a rectangle are perpendicular and have opposite and reciprocal slopes.<br />
ID: A<br />
PTS: 2 REF: 061028ge STA: G.G.69 TOP: Quadril<strong>at</strong>erals in the Coordin<strong>at</strong>e Plane<br />
306 ANS: 3 PTS: 2 REF: 061004ge STA: G.G.31<br />
TOP: Isosceles Triangle Theorem<br />
307 ANS: 2<br />
2 + (−4)<br />
M x =<br />
2<br />
= −1. M Y =<br />
−3 + 6<br />
2<br />
= 3<br />
2 .<br />
PTS: 2 REF: fall0813ge STA: G.G.66 TOP: Midpoint<br />
KEY: general<br />
308 ANS: 2 PTS: 2 REF: 011006ge STA: G.G.56<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
309 ANS: 1<br />
Transl<strong>at</strong>ions and reflections do not affect distance.<br />
PTS: 2 REF: 080908ge STA: G.G.61<br />
TOP: Analytical Represent<strong>at</strong>ions of Transform<strong>at</strong>ions
310 ANS: 3 PTS: 2 REF: 080924ge STA: G.G.24<br />
TOP: Neg<strong>at</strong>ions<br />
311 ANS: 3<br />
. The sum of the interior angles of a pentagon is (5 − 2)180 = 540.<br />
ID: A<br />
PTS: 2<br />
312 ANS: 2<br />
3 6<br />
=<br />
7 x<br />
REF: 011023ge STA: G.G.36 TOP: Interior and Exterior Angles of Polygons<br />
3x = 42<br />
x = 14<br />
PTS: 2 REF: 081027ge STA: G.G.46 TOP: Side Splitter Theorem<br />
313 ANS: 2 PTS: 2 REF: 011020ge STA: G.G.74<br />
TOP: Graphing Circles<br />
314 ANS: 2<br />
(d + 4)4 = 12(6)<br />
4d + 16 = 72<br />
d = 14<br />
r = 7<br />
PTS: 2 REF: 061023ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: two secants<br />
315 ANS: 1<br />
The centroid divides each median into segments whose lengths are in the r<strong>at</strong>io 2 : 1. GC = 2FG<br />
PTS: 2 REF: 081018ge STA: G.G.43 TOP: Centroid<br />
GC + FG = 24<br />
2FG + FG = 24<br />
3FG = 24<br />
FG = 8
316 ANS:<br />
ID: A<br />
AB CD and AD CB because their slopes are equal. ABCD is a parallelogram<br />
because opposite side are parallel. AB ≠ BC . ABCD is not a rhombus because all sides are not equal.<br />
AB ∼ ⊥ BC because their slopes are not opposite reciprocals. ABCD is not a rectangle because ∠ABC is not a<br />
right angle.<br />
PTS: 4 REF: 081038ge STA: G.G.69 TOP: Quadril<strong>at</strong>erals in the Coordin<strong>at</strong>e Plane<br />
317 ANS: 4<br />
L = 2πrh = 2π ⋅ 5 ⋅ 11 ≈ 345.6<br />
PTS: 2<br />
318 ANS: 2<br />
REF: 061006ge STA: G.G.14 TOP: Volume<br />
−2 + 6 −4 + 2<br />
M x = = 2. M y = = −1<br />
2<br />
2<br />
PTS: 2 REF: 080910ge STA: G.G.66 TOP: Midpoint<br />
KEY: general<br />
319 ANS: 1<br />
In an equil<strong>at</strong>eral triangle, each interior angle is 60° and each exterior angle is 120° (180° - 120°). The sum of the<br />
three interior angles is 180° and the sum of the three exterior angles is 360°.<br />
PTS: 2 REF: 060909ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles<br />
320 ANS:<br />
PTS: 2 REF: 060930ge STA: G.G.19 TOP: Constructions<br />
321 ANS: 3 PTS: 2 REF: 080928ge STA: G.G.50<br />
TOP: Tangents KEY: common tangency
322 ANS: 1<br />
A′(2,4)<br />
PTS: 2<br />
KEY: basic<br />
REF: 011023ge STA: G.G.54 TOP: Compositions of Transform<strong>at</strong>ions<br />
323 ANS: 1 PTS: 2 REF: 061005ge STA: G.G.55<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
324 ANS: 4<br />
SA = 4π r 2<br />
144π = 4π r 2<br />
V = 4<br />
3 π r 3 = 4<br />
3 π ⋅ 63 = 288π<br />
36 = r 2<br />
6 = r<br />
PTS: 2 REF: 081020ge STA: G.G.16 TOP: Surface Area<br />
325 ANS:<br />
ID: A<br />
FE ≅ FE (Reflexive Property); AE − FE ≅ FC − EF (Line Segment Subtraction<br />
Theorem); AF ≅ CE (Substitution); ∠BFA ≅ ∠DEC (All right angles are congruent); BFA ≅ DEC (AAS);<br />
AB ≅ CD and BF ≅ DE (CPCTC); ∠BFC ≅ ∠DEA (All right angles are congruent); BFC ≅ DEA (SAS);<br />
AD ≅ CB (CPCTC); ABCD is a parallelogram (opposite sides of quadril<strong>at</strong>eral ABCD are congruent)<br />
PTS: 6<br />
326 ANS: 4<br />
REF: 080938ge STA: G.G.41 TOP: Special Quadril<strong>at</strong>erals<br />
3y + 1 = 6x + 4.<br />
2y + 1 = x − 9<br />
3y = 6x + 3<br />
y = 2x + 1<br />
2y = x − 10<br />
y = 1<br />
x − 5<br />
2<br />
PTS: 2 REF: fall0822ge STA: G.G.63 TOP: Parallel and Perpendicular Lines
327 ANS: 1<br />
4x = 6 ⋅ 10<br />
x = 15<br />
PTS: 2 REF: 081017ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: two chords<br />
328 ANS: 1<br />
(n − 2)180<br />
∠A = =<br />
n<br />
(5 − 2)180<br />
5<br />
= 108 ∠AEB =<br />
180 − 108<br />
2<br />
= 36<br />
ID: A<br />
PTS: 2<br />
329 ANS:<br />
REF: 081022ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons<br />
2016. V = 1 1<br />
Bh =<br />
3 3 s2 h = 1<br />
3 122 ⋅ 42 = 2016<br />
PTS: 2 REF: 080930ge STA: G.G.13 TOP: Volume<br />
330 ANS:<br />
25. d = (−3 − 4) 2 + (1 − 25) 2 = 49 + 576 = 625 = 25.<br />
PTS: 2 REF: fall0831ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
331 ANS: 2 PTS: 2 REF: 061007ge STA: G.G.35<br />
TOP: Parallel Lines and Transversals<br />
332 ANS: 2 PTS: 2 REF: 061002ge STA: G.G.24<br />
TOP: Neg<strong>at</strong>ions<br />
333 ANS: 1<br />
a 2 + (5 2) 2 = (2 15) 2<br />
a 2 + (25 × 2) = 4 × 15<br />
a 2 + 50 = 60<br />
a 2 = 10<br />
a = 10<br />
PTS: 2 REF: 011016ge STA: G.G.48 TOP: Pythagorean Theorem
334 ANS: 4<br />
d = (−3 − 1) 2 + (2 − 0) 2 = 16 + 4 = 20 = 4 ⋅ 5 = 2 5<br />
PTS: 2 REF: 011017ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
335 ANS: 4 PTS: 2 REF: 060913ge STA: G.G.26<br />
TOP: Conditional St<strong>at</strong>ements<br />
336 ANS: 2<br />
Parallel chords intercept congruent arcs. mAC = mBD = 30. 180 − 30 − 30 = 120.<br />
PTS: 2<br />
337 ANS: 3<br />
REF: 080904ge STA: G.G.52 TOP: Chords<br />
The slope of y = x + 2 is 1. The slope of y − x = −1 is −A −(−1)<br />
= = 1.<br />
B 1<br />
ID: A<br />
PTS: 2 REF: 080909ge STA: G.G.63 TOP: Parallel and Perpendicular Lines<br />
338 ANS: 1<br />
After the transl<strong>at</strong>ion, the coordin<strong>at</strong>es are A′(−1,5) and B′(3,4). After the dil<strong>at</strong>ion, the coordin<strong>at</strong>es are A″(−2,10)<br />
and B″(6,8).<br />
PTS: 2 REF: fall0823ge STA: G.G.58 TOP: Compositions of Transform<strong>at</strong>ions<br />
339 ANS: 3<br />
4(x + 4) = 8 2<br />
4x + 16 = 64<br />
x = 12<br />
PTS: 2 REF: 060916ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: tangent and secant<br />
340 ANS: 4 PTS: 2 REF: 061018ge STA: G.G.56<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
341 ANS: 4<br />
Longest side of a triangle is opposite the largest angle. Shortest side is opposite the smallest angle.<br />
PTS: 2 REF: 081011ge STA: G.G.34 TOP: Angle Side Rel<strong>at</strong>ionship<br />
342 ANS: 2<br />
x 2 = 3(x + 18)<br />
x 2 − 3x − 54 = 0<br />
(x − 9)(x + 6) = 0<br />
x = 9<br />
PTS: 2 REF: fall0817ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: tangent and secant
343 ANS: 3<br />
2y = −6x + 8<br />
y = −3x + 4<br />
m = −3<br />
m ⊥ = 1<br />
3<br />
Perpendicular lines have slope the opposite and reciprocal of each other.<br />
PTS: 2 REF: 081024ge STA: G.G.62 TOP: Parallel and Perpendicular Lines<br />
344 ANS:<br />
BD ≅ DB (Reflexive Property); ABD ≅ CDB (SSS); ∠BDC ≅ ∠ABD (CPCTC).<br />
PTS: 4 REF: 061035ge STA: G.G.27 TOP: Quadril<strong>at</strong>eral Proofs<br />
345 ANS: 1 PTS: 2 REF: 061009ge STA: G.G.26<br />
TOP: Converse and Biconditional<br />
346 ANS:<br />
(6,−4). C x = Q x + R x<br />
2<br />
3.5 = 1 + R x<br />
2<br />
7 = 1 + R x<br />
6 = R x<br />
. C y = Q y + R y<br />
2<br />
8 + R y<br />
2 =<br />
2<br />
4 = 8 + R y<br />
−4 = R y<br />
PTS: 2<br />
KEY: graph<br />
347 ANS: 2<br />
REF: 011031ge STA: G.G.66 TOP: Midpoint<br />
y + 1<br />
x = 4<br />
2<br />
3x + 6y = 12<br />
y = − 1<br />
x + 4<br />
2<br />
m = − 1<br />
2<br />
6y = −3x + 12<br />
y = − 3<br />
x + 2<br />
6<br />
y = − 1<br />
x + 2<br />
2<br />
.<br />
PTS: 2 REF: 081014ge STA: G.G.63 TOP: Parallel and Perpendicular Lines<br />
ID: A
348 ANS: 3<br />
ID: A<br />
PTS: 2<br />
349 ANS: 1<br />
REF: 060902ge STA: G.G.28 TOP: Triangle Congruency<br />
−2 + 6 3 + 3<br />
M x = = 2. M y = = 3. The center is (2,3). d =<br />
2<br />
2<br />
(−2 − 6) 2 + (3 − 3) 2 is 8, the radius is 4 and r<br />
= 64 + 0 = 8. If the diameter<br />
2 = 16.<br />
PTS: 2<br />
350 ANS: 4<br />
REF: fall0820ge STA: G.G.71 TOP: Equ<strong>at</strong>ions of Circles<br />
The slope of a line in standard form is − A<br />
−4<br />
, so the slope of this line is = −2. A parallel line would also have a<br />
B 2<br />
slope of −2. Since the answers are in slope intercept form, find the y-intercept: y = mx + b<br />
3 = −2(7) + b<br />
17 = b<br />
PTS: 2 REF: 081010ge STA: G.G.65 TOP: Parallel and Perpendicular Lines<br />
351 ANS: 4<br />
(4) is not true if ∠PQR is obtuse.<br />
PTS: 2 REF: 060924ge STA: G.G.32 TOP: Exterior Angle Theorem<br />
352 ANS: 1<br />
If ∠A is <strong>at</strong> minimum (50°) and ∠B is <strong>at</strong> minimum (90°), ∠C is <strong>at</strong> maximum of 40° (180° - (50° + 90°)). If ∠A is<br />
<strong>at</strong> maximum (60°) and ∠B is <strong>at</strong> maximum (100°), ∠C is <strong>at</strong> minimum of 20° (180° - (60° + 100°)).<br />
PTS: 2 REF: 060901ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles<br />
353 ANS: 1<br />
AB = 10 since ABC is a 6-8-10 triangle. 6 2 = 10x<br />
3.6 = x<br />
PTS: 2 REF: 060915ge STA: G.G.47 TOP: Similarity<br />
KEY: leg<br />
354 ANS: 1 PTS: 2 REF: 081009ge STA: G.G.73<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
355 ANS:<br />
6. The centroid divides each median into segments whose lengths are in the r<strong>at</strong>io 2 : 1. TD = 6 and DB = 3<br />
PTS: 2 REF: 011034ge STA: G.G.43 TOP: Centroid
356 ANS:<br />
AC. m∠BCA = 63 and m∠ABC = 80. AC is the longest side as it is opposite the largest angle.<br />
PTS: 2 REF: 080934ge STA: G.G.34 TOP: Angle Side Rel<strong>at</strong>ionship<br />
357 ANS: 1<br />
PTS: 2 REF: 081003ge STA: G.G.42 TOP: Midsegments<br />
358 ANS: 2<br />
x 2 + (x + 7) 2 = 13 2<br />
x 2 + x 2 + 7x + 7x + 49 = 169<br />
2x 2 + 14x − 120 = 0<br />
x 2 + 7x − 60 = 0<br />
(x + 12)(x − 5) = 0<br />
x = 5<br />
2x = 10<br />
PTS: 2 REF: 061024ge STA: G.G.48 TOP: Pythagorean Theorem<br />
359 ANS:<br />
PTS: 4 REF: fall0837ge STA: G.G.23 TOP: Locus<br />
360 ANS: 4 PTS: 2 REF: 061008ge STA: G.G.40<br />
TOP: Trapezoids<br />
ID: A
361 ANS: 2<br />
7 + 18 > 6 + 12<br />
PTS: 2 REF: fall0819ge STA: G.G.33 TOP: Triangle Inequality Theorem<br />
362 ANS: 1 PTS: 2 REF: fall0807ge STA: G.G.19<br />
TOP: Constructions<br />
363 ANS: 1 PTS: 2 REF: 060920ge STA: G.G.74<br />
TOP: Graphing Circles<br />
364 ANS: 4 PTS: 2 REF: 060922ge STA: G.G.73<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
365 ANS: 1<br />
Since AC ≅ BC , m∠A = m∠B under the Isosceles Triangle Theorem.<br />
PTS: 2 REF: fall0809ge STA: G.G.69 TOP: Triangles in the Coordin<strong>at</strong>e Plane<br />
366 ANS: 3<br />
V = πr 2 h = π ⋅ 6 2 ⋅ 27 = 972π<br />
PTS: 2 REF: 011027ge STA: G.G.14 TOP: Volume<br />
367 ANS: 4<br />
d = (−6 − 2) 2 + (4 − (−5)) 2 = 64 + 81 = 145<br />
ID: A<br />
PTS: 2 REF: 081013ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
368 ANS: 1 PTS: 2 REF: 061214ge STA: G.G.21<br />
TOP: Centroid, Orthocenter, Incenter and Circumcenter<br />
369 ANS: 1 PTS: 2 REF: 061010ge STA: G.G.34<br />
TOP: Angle Side Rel<strong>at</strong>ionship<br />
370 ANS: 4<br />
The marked 60º angle and the angle above it are on the same straight line and supplementary. This unmarked<br />
supplementary angle is 120º. Because the unmarked 120º angle and the marked 120º angle are altern<strong>at</strong>e exterior<br />
angles and congruent, d e.<br />
PTS: 2 REF: 080901ge STA: G.G.35 TOP: Parallel Lines and Transversals<br />
371 ANS:<br />
5. 3<br />
x<br />
= 6 + 3<br />
15<br />
9x = 45<br />
x = 5<br />
PTS: 2 REF: 011033ge STA: G.G.46 TOP: Side Splitter Theorem<br />
372 ANS: 3 PTS: 2 REF: 060928ge STA: G.G.8<br />
TOP: Planes
373 ANS:<br />
2 3. x 2 = 3 ⋅ 4<br />
x = 12 = 2 3<br />
PTS: 2 REF: fall0829ge STA: G.G.47 TOP: Similarity<br />
KEY: altitude<br />
374 ANS: 4<br />
BG is also an angle bisector since it intersects the concurrence of CD and AE<br />
PTS: 2 REF: 061025ge STA: G.G.21<br />
KEY: Centroid, Orthocenter, Incenter and Circumcenter<br />
375 ANS: 2<br />
A dil<strong>at</strong>ion affects distance, not angle measure.<br />
PTS: 2 REF: 080906ge STA: G.G.60 TOP: Identifying Transform<strong>at</strong>ions<br />
376 ANS: 4<br />
180 − (40 + 40) = 100<br />
PTS: 2<br />
377 ANS:<br />
REF: 080903ge STA: G.G.31 TOP: Isosceles Triangle Theorem<br />
18. V = 1 1<br />
Bh =<br />
3 3 lwh<br />
288 = 1<br />
⋅ 8 ⋅ 6 ⋅ h<br />
3<br />
288 = 16h<br />
18 = h<br />
PTS: 2 REF: 061034ge STA: G.G.13 TOP: Volume<br />
378 ANS: 4<br />
The radius is 4. r 2 = 16.<br />
PTS: 2<br />
379 ANS: 3<br />
REF: 061014ge STA: G.G.72 TOP: Equ<strong>at</strong>ions of Circles<br />
The diagonals of an isosceles trapezoid are congruent. 5x + 3 = 11x − 5.<br />
6x = 18<br />
x = 3<br />
PTS: 2 REF: fall0801ge STA: G.G.40 TOP: Trapezoids<br />
ID: A
380 ANS:<br />
PTS: 6 REF: 011038ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
381 ANS: 3<br />
m = −A<br />
B<br />
= −3<br />
4<br />
PTS: 2 REF: 011025ge STA: G.G.62 TOP: Parallel and Perpendicular Lines<br />
382 ANS: 1 PTS: 2 REF: 081008ge STA: G.G.3<br />
TOP: Planes<br />
383 ANS: 4 PTS: 2 REF: fall0818ge STA: G.G.61<br />
TOP: Analytical Represent<strong>at</strong>ions of Transform<strong>at</strong>ions<br />
384 ANS: 2<br />
4(4x − 3) = 3(2x + 8)<br />
16x − 12 = 6x + 24<br />
10x = 36<br />
x = 3.6<br />
PTS: 2 REF: 080923ge STA: G.G.53 TOP: Segments Intercepted by Circle<br />
KEY: two chords<br />
385 ANS: 1<br />
3x 2 + 18x + 24<br />
3(x 2 + 6x + 8)<br />
3(x + 4)(x + 2)<br />
PTS: 2 REF: fall0815ge STA: G.G.12 TOP: Volume<br />
386 ANS: 3 PTS: 2 REF: 080902ge STA: G.G.17<br />
TOP: Constructions<br />
ID: A
387 ANS:<br />
PTS: 2 REF: fall0832ge STA: G.G.17 TOP: Constructions<br />
388 ANS: 3 PTS: 2 REF: fall0804ge STA: G.G.18<br />
TOP: Constructions<br />
389 ANS:<br />
3. The non-parallel sides of an isosceles trapezoid are congruent. 2x + 5 = 3x + 2<br />
x = 3<br />
PTS: 2 REF: 080929ge STA: G.G.40 TOP: Trapezoids<br />
390 ANS:<br />
(x + 1) 2 + (y − 2) 2 = 36<br />
PTS: 2<br />
391 ANS: 4<br />
REF: 081034ge STA: G.G.72 TOP: Equ<strong>at</strong>ions of Circles<br />
The slope of y = −3x + 2 is −3. The perpendicular slope is 1 1<br />
. −1 = (3) + b<br />
3 3<br />
−1 = 1 + b<br />
b = −2<br />
PTS: 2 REF: 011018ge STA: G.G.64 TOP: Parallel and Perpendicular Lines<br />
392 ANS: 3 PTS: 2 REF: 060908ge STA: G.G.60<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
393 ANS: 2 PTS: 2 REF: 061020ge STA: G.G.19<br />
TOP: Constructions<br />
394 ANS: 1 PTS: 2 REF: 081012ge STA: G.G.50<br />
TOP: Tangents KEY: two tangents<br />
395 ANS: 2 PTS: 2 REF: 081015ge STA: G.G.55<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
396 ANS: 4<br />
d = (146 − (−4)) 2 + (52 − 2) 2 = 25,000 ≈ 158.1<br />
PTS: 2 REF: 061021ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
397 ANS: 2 PTS: 2 REF: 080921ge STA: G.G.72<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
ID: A
398 ANS: 1<br />
−2 − 1 <br />
<br />
y = 6x + 10<br />
<br />
2<br />
<br />
y = −12x − 20<br />
PTS: 2 REF: 061027ge STA: G.G.63 TOP: Parallel and Perpendicular Lines<br />
399 ANS: 1<br />
The closer a chord is to the center of a circle, the longer the chord.<br />
PTS: 2 REF: 011005ge STA: G.G.49 TOP: Chords<br />
400 ANS: 3<br />
36 − 20<br />
= 8. 17<br />
2<br />
2 − 8 2 = 15<br />
PTS: 2 REF: 061016ge STA: G.G.40 TOP: Trapezoids<br />
401 ANS:<br />
y = 2<br />
x + 1. 2y + 3x = 6<br />
3<br />
2y = −3x + 6<br />
y = − 3<br />
x + 3<br />
2<br />
m = − 3<br />
2<br />
m⊥ = 2<br />
3<br />
. y = mx + b<br />
5 = 2<br />
(6) + b<br />
3<br />
5 = 4 + b<br />
1 = b<br />
y = 2<br />
x + 1<br />
3<br />
PTS: 4 REF: 061036ge STA: G.G.64 TOP: Parallel and Perpendicular Lines<br />
402 ANS: 4 PTS: 2 REF: fall0824ge STA: G.G.50<br />
TOP: Tangents<br />
403 ANS: 2<br />
KEY: common tangency<br />
Because the triangles are similar, m∠A<br />
= 1<br />
m∠D<br />
PTS: 2 REF: 011022ge STA: G.G.45 TOP: Similarity<br />
KEY: perimeter and area<br />
ID: A
404 ANS:<br />
20. 5x + 10 = 4x + 30<br />
x = 20<br />
PTS: 2 REF: 060934ge STA: G.G.45 TOP: Similarity<br />
KEY: basic<br />
405 ANS: 1<br />
d = (−4 − 2) 2 + (5 − (−5)) 2 = 36 + 100 = 136 = 4 ⋅ 34 = 2 34 .<br />
PTS: 2 REF: 080919ge STA: G.G.67 TOP: Distance<br />
KEY: general<br />
406 ANS: 3 PTS: 2 REF: 080913ge STA: G.G.28<br />
TOP: Triangle Congruency<br />
407 ANS: 4<br />
ABC ∼ DBE. AB<br />
DB<br />
= AC<br />
DE<br />
9 x<br />
=<br />
2 3<br />
x = 13.5<br />
PTS: 2 REF: 060927ge STA: G.G.46 TOP: Side Splitter Theorem<br />
408 ANS: 3 PTS: 2 REF: 081021ge STA: G.G.57<br />
TOP: Properties of Transform<strong>at</strong>ions<br />
409 ANS: 3<br />
PTS: 2 REF: 061011ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
410 ANS: 3 PTS: 2 REF: 061017ge STA: G.G.1<br />
TOP: Planes<br />
ID: A
411 ANS:<br />
PTS: 2 REF: 061033ge STA: G.G.22 TOP: Locus<br />
412 ANS: 3 PTS: 2 REF: fall0825ge STA: G.G.21<br />
TOP: Centroid, Orthocenter, Incenter and Circumcenter<br />
413 ANS: 4 PTS: 2 REF: 081005ge STA: G.G.18<br />
TOP: Constructions<br />
414 ANS: 4<br />
y + x = 4<br />
y = −x + 4<br />
. x 2 − 6x + 10 = −x + 4.<br />
y + x = 4.<br />
y + 2 = 4<br />
x 2 − 5x + 6 = 0<br />
(x − 3)(x − 2) = 0<br />
x = 3 or 2<br />
y + 3 = 4<br />
y = 1<br />
PTS: 2<br />
415 ANS: 4<br />
REF: 080912ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems<br />
−6 + 1<br />
M x = = −<br />
2<br />
5<br />
2 . M 1 + 8<br />
y = =<br />
2<br />
9<br />
2 .<br />
y = 2<br />
PTS: 2 REF: 060919ge STA: G.G.66 TOP: Midpoint<br />
KEY: graph<br />
416 ANS: 1<br />
PRT and SRQ share ∠R and it is given th<strong>at</strong> ∠RPT ≅ ∠RSQ.<br />
PTS: 2 REF: fall0821ge STA: G.G.44 TOP: Similarity Proofs<br />
ID: A
417 ANS:<br />
PTS: 2 REF: 081032ge STA: G.G.20 TOP: Constructions<br />
418 ANS: 1 PTS: 2 REF: 081028ge STA: G.G.21<br />
TOP: Centroid, Orthocenter, Incenter and Circumcenter<br />
419 ANS: 2<br />
6 + 17 > 22<br />
PTS: 2 REF: 080916ge STA: G.G.33 TOP: Triangle Inequality Theorem<br />
420 ANS:<br />
−4 + 4<br />
Midpoint: ,<br />
2<br />
2 + (−4)<br />
<br />
<br />
2<br />
<br />
<br />
= (0,−1). Distance: d = (−4 − 4)2 + (2 − (−4)) 2 r = 5<br />
= 100 = 10<br />
x 2 + (y + 1) 2 = 25<br />
r 2 = 25<br />
PTS: 4 REF: 061037ge STA: G.G.71 TOP: Equ<strong>at</strong>ions of Circles<br />
421 ANS:<br />
20. The sides of the triangle formed by connecting the midpoints are half the sides of the original triangle.<br />
5 + 7 + 8 = 20.<br />
PTS: 2 REF: 060929ge STA: G.G.42 TOP: Midsegments<br />
422 ANS: 2<br />
The slope of a line in standard form is − A<br />
B<br />
the opposite and reciprocal of each other.<br />
so the slope of this line is −5<br />
3<br />
ID: A<br />
Perpendicular lines have slope th<strong>at</strong> are<br />
PTS: 2 REF: fall0828ge STA: G.G.62 TOP: Parallel and Perpendicular Lines
423 ANS:<br />
PTS: 2<br />
424 ANS: 1<br />
REF: 080932ge STA: G.G.17 TOP: Constructions<br />
V = 1<br />
3 πr 2 h = 1<br />
3 π ⋅ 42 ⋅ 12 ≈ 201<br />
PTS: 2 REF: 060921ge STA: G.G.15 TOP: Volume<br />
425 ANS: 4<br />
sum of interior ∠s = sum of exterior ∠s<br />
<br />
(n − 2)180 = n 180 −<br />
<br />
(n − 2)180<br />
n<br />
180n − 360 = 180n − 180n + 360<br />
180n = 720<br />
n = 4<br />
<br />
<br />
ID: A<br />
PTS: 2 REF: 081016ge STA: G.G.36 TOP: Interior and Exterior Angles of Polygons<br />
426 ANS: 2 PTS: 2 REF: 061022ge STA: G.G.62<br />
TOP: Parallel and Perpendicular Lines<br />
427 ANS: 2<br />
The slope of 2x + 3y = 12 is − A<br />
B<br />
(2) becomes y = 3<br />
x + 3.<br />
2<br />
= − 2<br />
3<br />
3<br />
. The slope of a perpendicular line is . Rewritten in slope intercept form,<br />
2<br />
PTS: 2 REF: 060926ge STA: G.G.63 TOP: Parallel and Perpendicular Lines<br />
428 ANS: 4 PTS: 2 REF: 081023ge STA: G.G.45<br />
TOP: Similarity KEY: perimeter and area<br />
429 ANS: 3<br />
The l<strong>at</strong>eral edges of a prism are parallel.<br />
PTS: 2 REF: fall0808ge STA: G.G.10 TOP: Solids<br />
430 ANS: 2<br />
Longest side of a triangle is opposite the largest angle. Shortest side is opposite the smallest angle.<br />
PTS: 2 REF: 060911ge STA: G.G.34 TOP: Angle Side Rel<strong>at</strong>ionship
431 ANS:<br />
D′(−1,1), E ′(−1,5), G′(−4,5)<br />
PTS: 4 REF: 080937ge STA: G.G.55 TOP: Properties of Transform<strong>at</strong>ions<br />
432 ANS: 1 PTS: 2 REF: 061012ge STA: G.G.20<br />
TOP: Constructions<br />
433 ANS: 2<br />
The length of the midsegment of a trapezoid is the average of the lengths of its bases.<br />
PTS: 2 REF: 011001ge STA: G.G.40 TOP: Trapezoids<br />
434 ANS: 4 PTS: 2 REF: 080905ge STA: G.G.29<br />
TOP: Triangle Congruency<br />
435 ANS: 3 PTS: 2 REF: 060905ge STA: G.G.54<br />
TOP: Reflections KEY: basic<br />
436 ANS: 1<br />
3x + 15 + 2x − 1 = 6x + 2<br />
5x + 14 = 6x + 2<br />
x = 12<br />
x + 30<br />
2<br />
= 44.<br />
x + 30 = 88<br />
x = 58<br />
PTS: 2 REF: 011021ge STA: G.G.32 TOP: Exterior Angle Theorem<br />
437 ANS:<br />
26. x + 3x + 5x − 54 = 180<br />
9x = 234<br />
x = 26<br />
ID: A<br />
PTS: 2 REF: 080933ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles
438 ANS: 2<br />
The centroid divides each median into segments whose lengths are in the r<strong>at</strong>io 2 : 1.<br />
PTS: 2 REF: 060914ge STA: G.G.43 TOP: Centroid<br />
439 ANS: 2 PTS: 2 REF: 011011ge STA: G.G.22<br />
TOP: Locus<br />
440 ANS:<br />
22.4. V = πr 2 h<br />
12566.4 = πr 2 ⋅ 8<br />
r 2 = 12566.4<br />
8π<br />
r ≈ 22.4<br />
PTS: 2 REF: fall0833ge STA: G.G.14 TOP: Volume<br />
441 ANS: 3 PTS: 2 REF: 081002ge STA: G.G.9<br />
TOP: Planes<br />
442 ANS: 3<br />
m = −A<br />
B<br />
5 −A 10 5<br />
= . m = = =<br />
2 B 4 2<br />
PTS: 2 REF: 011014ge STA: G.G.63 TOP: Parallel and Perpendicular Lines<br />
443 ANS: 1 PTS: 2 REF: 060918ge STA: G.G.2<br />
TOP: Planes<br />
444 ANS:<br />
PTS: 2 REF: 061130ge STA: G.G.20 TOP: Constructions<br />
ID: A
445 ANS:<br />
∠D, ∠G and 24° or ∠E, ∠F and 84°. mFE = 2<br />
× 360 = 48. Since the chords forming ∠D and ∠G are<br />
15<br />
intercepted by FE, their measure is 24°. mGD = 7<br />
× 360 = 168. Since the chords forming ∠E and ∠F are<br />
15<br />
intercepted by GD, their measure is 84°.<br />
ID: A<br />
PTS: 4 REF: fall0836ge STA: G.G.51 TOP: Arcs Determined by Angles<br />
KEY: inscribed<br />
446 ANS: 4 PTS: 2 REF: 011019ge STA: G.G.44<br />
TOP: Similarity Proofs<br />
447 ANS: 3 PTS: 2 REF: 011010ge STA: G.G.71<br />
TOP: Equ<strong>at</strong>ions of Circles<br />
448 ANS: 1<br />
∠DCB and ∠ADC are supplementary adjacent angles of a parallelogram. 180 − 120 = 60. ∠2 = 60 − 45 = 15.<br />
PTS: 2 REF: 080907ge STA: G.G.38 TOP: Parallelograms<br />
449 ANS: 1<br />
(x,y) → (x + 3,y + 1)<br />
PTS: 2 REF: fall0803ge STA: G.G.54 TOP: Transl<strong>at</strong>ions<br />
450 ANS:<br />
JK ≅ LM because opposite sides of a parallelogram are congruent. LM ≅ LN because of the Isosceles Triangle<br />
Theorem. LM ≅ JM because of the transitive property. JKLM is a rhombus because all sides are congruent.<br />
PTS: 4 REF: 011036ge STA: G.G.41 TOP: Special Quadril<strong>at</strong>erals<br />
451 ANS: 4 PTS: 2 REF: fall0802ge STA: G.G.24<br />
TOP: Neg<strong>at</strong>ions<br />
452 ANS: 1 PTS: 2 REF: 060903ge STA: G.G.56<br />
TOP: Identifying Transform<strong>at</strong>ions<br />
453 ANS: 1 PTS: 2 REF: 061013ge STA: G.G.50<br />
TOP: Tangents KEY: point of tangency<br />
454 ANS: 3 PTS: 2 REF: 060925ge STA: G.G.17<br />
TOP: Constructions<br />
455 ANS: 3<br />
PTS: 2 REF: fall0805ge STA: G.G.70 TOP: Quadr<strong>at</strong>ic-Linear Systems
456 ANS:<br />
PTS: 2 REF: 060932ge STA: G.G.22 TOP: Locus<br />
ID: A