Geometry Regents at Random Worksheets - JMap

Geometry Regents Exam Questions at Random Worksheet # 1 NAME:________________________________ 

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Geometry Regents at Random Worksheets 

1 Solve the following system of equations 

graphically. 

2x 2 − 4x = y + 1 

x + y = 1 

2 In circle O, a diameter has endpoints (−5,4) and 

(3,−6). What is the length of the diameter? 

1) 2 

2) 2 2 

3) 10 

4) 2 41 

3 Which statement is the negation of “Two is a prime 

number” and what is the truth value of the 

negation? 

1) Two is not a prime number; false 

2) Two is not a prime number; true 

3) A prime number is two; false 

4) A prime number is two; true 

4 In DEF, m∠D = 3x + 5, m∠E = 4x − 15, and 

m∠F = 2x + 10. Which statement is true? 

1) DF = FE 

2) DE = FE 

3) m∠E = m∠F 

4) m∠D = m∠F 

5 In the diagram below of quadrilateral ABCD, 

AD ≅ BC and ∠DAE ≅ ∠BCE. Line segments 

AC, DB, and FG intersect at E. 

Prove: AEF ≅ CEG 

6 The volume of a rectangular prism is 144 cubic 

inches. The height of the prism is 8 inches. Which 

measurements, in inches, could be the dimensions 

of the base? 

1) 3.3 by 5.5 

2) 2.5 by 7.2 

3) 12 by 8 

4) 9 by 9


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7 In the diagram below of ACD, B is a point on 

AC such that ADB is an equilateral triangle, and 

DBC is an isosceles triangle with DB ≅ BC . 

Find m∠C. 

8 As shown on the graph below, R′S ′T ′ is the 

image of RST under a single transformation. 

Which transformation does this graph represent? 

1) glide reflection 

2) line reflection 

3) rotation 

4) translation 

9 The diagram below shows a rectangular prism. 

Which pair of edges are segments of lines that are 

coplanar? 

1) AB and DH 

2) AE and DC 

3) BC and EH 

4) CG and EF 

10 .A straightedge and compass were used to create 

the construction below. Arc EF was drawn from 

point B, and arcs with equal radii were drawn from 

E and F. 

Which statement is false? 

1) m∠ABD = m∠DBC 

2) 

1 

(m∠ABC) = m∠ABD 

2 

3) 2(m∠DBC) = m∠ABC 

4) 2(m∠ABC) = m∠CBD


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11 Which graph represents a circle whose equation is 

(x + 2) 2 + y 2 = 16? 

1) 

2) 

3) 

4) 

12 In the diagram below of ABC, D is a point on 

AB, E is a point on BC , AC DE, CE = 25 inches, 

AD = 18 inches, and DB = 12 inches. Find, to the 

nearest tenth of an inch, the length of EB. 

13 Using a compass and straightedge, construct a line 

perpendicular to AB through point P. [Leave all 

construction marks.]


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14 Which line is parallel to the line whose equation is 

4x + 3y = 7 and also passes through the point 

(−5,2)? 

1) 4x + 3y = −26 

2) 4x + 3y = −14 

3) 3x + 4y = −7 

4) 3x + 4y = 14 

15 The cylindrical tank shown in the diagram below is 

to be painted. The tank is open at the top, and the 

bottom does not need to be painted. Only the 

outside needs to be painted. Each can of paint 

covers 600 square feet. How many cans of paint 

must be purchased to complete the job? 

16 Which equation represents the perpendicular 

bisector of AB whose endpoints are A(8,2) and 

B(0,6)? 

1) y = 2x − 4 

2) y = − 1 

x + 2 

2 

3) y = − 1 

x + 6 

2 

4) y = 2x − 12 

17 What is the equation of the line that passes through 

the point (−9,6) and is perpendicular to the line 

y = 3x − 5? 

1) y = 3x + 21 

2) y = − 1 

x − 3 

3 

3) y = 3x + 33 

4) y = − 1 

x + 3 

3 

18 Triangle ABC has vertices A(−2,2), B(−1,−3), and 

C(4,0). Find the coordinates of the vertices of 

A′B′C ′, the image of ABC after the 

transformation r x-axis . [The use of the grid is 

optional.]


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19 In the diagram below, line p intersects line m and 

line n. 

If m∠1 = 7x and m∠2 = 5x + 30, lines m and n are 

parallel when x equals 

1) 12.5 

2) 15 

3) 87.5 

4) 105 

20 Find, in degrees, the measures of both an interior 

angle and an exterior angle of a regular pentagon. 

21 In the diagram below, ABC ≅ XYZ. 

Which statement must be true? 

1) ∠C ≅ ∠Y 

2) ∠A ≅ ∠X 

3) AC ≅ YZ 

4) CB ≅ XZ 

22 Given that ABCD is a parallelogram, a student 

wrote the proof below to show that a pair of its 

opposite angles are congruent. 

What is the reason justifying that ∠B ≅ ∠D? 

1) Opposite angles in a quadrilateral are 

congruent. 

2) Parallel lines have congruent corresponding 

angles. 

3) Corresponding parts of congruent triangles are 

congruent. 

4) Alternate interior angles in congruent triangles 

are congruent. 

23 In the diagram below of ADE, B is a point on AE 

and C is a point on AD such that BC ED, 

AC = x − 3, BE = 20, AB = 16, and AD = 2x + 2. 

Find the length of AC.


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24 On the diagram below, use a compass and 

straightedge to construct the bisector of ∠ABC. 

[Leave all construction marks.] 

25 The coordinates of trapezoid ABCD are A(−4,5), 

B(1,5), C(1,2), and D(−6,2). Trapezoid 

A″B″C ″D″ is the image after the composition 

r x − axis r y = x is performed on trapezoid ABCD. 

State the coordinates of trapezoid A″B″C ″D″. 

[The use of the set of axes below is optional.] 

26 For which polygon does the sum of the measures of 

the interior angles equal the sum of the measures of 

the exterior angles? 

1) hexagon 

2) pentagon 

3) quadrilateral 

4) triangle 

27 In the diagram below, ABC ∼ DEF, DE = 4, 

AB = x, AC = x + 2, and DF = x + 6. Determine the 

length of AB. [Only an algebraic solution can 

receive full credit.] 

28 Point M is the midpoint of AB. If the coordinates 

of A are (−3,6) and the coordinates of M are (−5,2), 

what are the coordinates of B? 

1) (1,2) 

2) (7,10) 

3) (−4,4) 

4) (−7,−2) 

29 Which statement is true about every parallelogram? 

1) All four sides are congruent. 

2) The interior angles are all congruent. 

3) Two pairs of opposite sides are congruent. 

4) The diagonals are perpendicular to each other.


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30 Which graph represents a circle with the equation 

(x − 3) 2 + (y + 1) 2 = 4? 

1) 

2) 

3) 

4) 

31 In the diagram below, BFCE, AB ⊥ BE , 

DE ⊥ BE , and ∠BFD ≅ ∠ECA. Prove that 

ABC ∼ DEF. 

32 In the diagram below, point M is located on AB → ←⎯ 

. 

Sketch the locus of points that are 1 unit from AB → ←⎯ 

and the locus of points 2 units from point M. Label 

with an X all points that satisfy both conditions. 

33 For a triangle, which two points of concurrence 

could be located outside the triangle? 

1) incenter and centroid 

2) centroid and orthocenter 

3) incenter and circumcenter 

4) circumcenter and orthocenter


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34 In the diagram below of ABC, D is the midpoint 

of AB, and E is the midpoint of BC . 

If AC = 4x + 10, which expression represents DE? 

1) x + 2.5 

2) 2x + 5 

3) 2x + 10 

4) 8x + 20 

35 In the diagram below, parallelogram ABCD has 

diagonals AC and BD that intersect at point E. 

Which expression is not always true? 

1) ∠DAE ≅ ∠BCE 

2) ∠DEC ≅ ∠BEA 

3) AC ≅ DB 

4) DE ≅ EB 

36 What is an equation of the line that passes through 

the point (−2,3) and is parallel to the line whose 

equation is y = 3 

x − 4? 

2 

1) y = −2 

3 x 

2) y = −2 

3 

3) y = 3 

2 x 

x + 5 

3 

4) y = 3 

x + 6 

2 

37 If two distinct planes, A and B, are perpendicular 

to line c, then which statement is true? 

1) Planes A and B are parallel to each other. 

2) Planes A and B are perpendicular to each 

other. 

3) The intersection of planes A and B is a line 

parallel to line c. 

4) The intersection of planes A and B is a line 

perpendicular to line c. 

38 A student wrote the sentence “4 is an odd integer.” 

What is the negation of this sentence and the truth 

value of the negation? 

1) 3 is an odd integer; true 

2) 4 is not an odd integer; true 

3) 4 is not an even integer; false 

4) 4 is an even integer; false


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39 In the diagram below of circle O, radius OC is 5 

cm. Chord AB is 8 cm and is perpendicular to OC 

at point P. 

What is the length of OP, in centimeters? 

1) 8 

2) 2 

3) 3 

4) 4 

40 In the diagram below, LATE is an isosceles 

trapezoid with LE ≅ AT, LA = 24, ET = 40, and 

AT = 10. Altitudes LF and AG are drawn. 

What is the length of LF? 

1) 6 

2) 8 

3) 3 

4) 4 

41 Segment AB is the diameter of circle M. The 

coordinates of A are (−4,3). The coordinates of M 

are (1,5). What are the coordinates of B? 

1) (6,7) 

2) (5,8) 

3) (−3,8) 

4) (−5,2) 

42 Using a compass and straightedge, construct the 

bisector of ∠CBA. [Leave all construction marks.] 

43 In the diagram below of ABC, side BC is 

extended to point D, m∠A = x, m∠B = 2x + 15, and 

m∠ACD = 5x + 5. 

What is m∠B? 

1) 5 

2) 20 

3) 25 

4) 55


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44 On the set of coordinate axes below, graph the 

locus of points that are equidistant from the lines 

y = 6 and y = 2 and also graph the locus of points 

that are 3 units from the y-axis. State the 

coordinates of all points that satisfy both 

conditions. 

45 What is the slope of a line that is perpendicular to 

the line represented by the equation x + 2y = 3? 

1) −2 

2) 2 

3) − 1 

4) 

1 

2 

2 

46 What is the measure of each interior angle of a 

regular hexagon? 

1) 60° 

2) 120° 

3) 135° 

4) 270° 

47 The angles of triangle ABC are in the ratio of 

8:3:4. What is the measure of the smallest angle? 

1) 12º 

2) 24º 

3) 36º 

4) 72º 

48 Chords AB and CD intersect at E in circle O, as 

shown in the diagram below. Secant FDA and 

tangent FB are drawn to circle O from external 

point F and chord AC is drawn. The mDA = 56, 

mDB = 112, and the ratio of mAC :mCB = 3:1. 

Determine m∠CEB. Determine m∠F . Determine 

m∠DAC . 

49 A paint can is in the shape of a right circular 

cylinder. The volume of the paint can is 600 

cubic inches and its altitude is 12 inches. Find the 

radius, in inches, of the base of the paint can. 

Express the answer in simplest radical form. Find, 

to the nearest tenth of a square inch, the lateral 

area of the paint can.


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50 In the diagram below of GJK, H is a point on 

GJ , HJ ≅ JK , m∠G = 28, and m∠GJK = 70. 

Determine whether GHK is an isosceles triangle 

and justify your answer. 

51 Pentagon PQRST has PQ parallel to TS. After a 

translation of T 2,−5 , which line segment is parallel 

to P ′Q′? 

1) R′Q′ 

2) R′S ′ 

3) T ′S ′ 

4) T ′P′ 

52 In ABC and DEF, AC CB 

= . Which 

DF FE 

additional information would prove 

ABC ∼ DEF? 

1) AC = DF 

2) CB = FE 

3) ∠ACB ≅ ∠DFE 

4) ∠BAC ≅ ∠EDF 

53 What is the image of the point (2,−3) after the 

transformation r y − axis ? 

1) (2,3) 

2) (−2,−3) 

3) (−2,3) 

4) (−3,2) 

54 Write the negation of the statement “2 is a prime 

number,” and determine the truth value of the 

negation. 

55 Given three distinct quadrilaterals, a square, a 

rectangle, and a rhombus, which quadrilaterals 

must have perpendicular diagonals? 

1) the rhombus, only 

2) the rectangle and the square 

3) the rhombus and the square 

4) the rectangle, the rhombus, and the square 

56 On the diagram of ABC shown below, use a 

compass and straightedge to construct the 

perpendicular bisector of AC. [Leave all 



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57 A man wants to place a new bird bath in his yard so 

that it is 30 feet from a fence, f, and also 10 feet 

from a light pole, P. As shown in the diagram 

below, the light pole is 35 feet away from the 

fence. 

How many locations are possible for the bird bath? 

1) 1 

2) 2 

3) 3 

4) 0 

58 As shown in the diagram below, AC bisects ∠BAD 

and ∠B ≅ ∠D. 

Which method could be used to prove 

ABC ≅ ADC? 

1) SSS 

2) AAA 

3) SAS 

4) AAS 

59 In the diagram below of circle O, chord AB is 

parallel to chord GH . Chord CD intersects AB at 

E and GH at F. 

Which statement must always be true? 

1) AC ≅ CB 

2) DH ≅ BH 

3) AB ≅ GH 

4) AG ≅ BH 

60 The coordinates of the endpoints of FG are (−4,3) 

and (2,5). Find the length of FG in simplest 

radical form. 

61 In FGH , m∠F = 42 and an exterior angle at 

vertex H has a measure of 104. What is m∠G? 

1) 34 

2) 62 

3) 76 

4) 146


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62 The coordinates of point A are (−3a,4b). If point 

A' is the image of point A reflected over the line 

y = x, the coordinates of A' are 

1) (4b,−3a) 

2) (3a,4b) 

3) (−3a,−4b) 

4) (−4b,−3a) 

63 A line segment has endpoints A(7,−1) and B(−3,3). 

What are the coordinates of the midpoint of AB? 

1) (1,2) 

2) 

 

2,1 

 

 

3) (−5,2) 

4) 

 

5,−2 

 

64 Plane A is parallel to plane B. Plane C intersects 

plane A in line m and intersects plane B in line n. 

Lines m and n are 

1) intersecting 

2) parallel 

3) perpendicular 

4) skew 

65 Which equation represents circle O with center 

(2,−8) and radius 9? 

1) (x + 2) 2 + (y − 8) 2 = 9 

2) (x − 2) 2 + (y + 8) 2 = 9 

3) (x + 2) 2 + (y − 8) 2 = 81 

4) (x − 2) 2 + (y + 8) 2 = 81 

66 Which diagram shows the construction of the 

perpendicular bisector of AB? 

1) 

2) 

3) 

4)


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67 In the diagram below, AB → ←⎯ 

AEFG. 

is perpendicular to plane 

Which plane must be perpendicular to plane 

AEFG? 

1) ABCE 

2) BCDH 

3) CDFE 

4) HDFG 

68 The sum of the interior angles of a polygon of n 

sides is 

1) 360 

2) 

360 

n 

3) (n − 2) ⋅ 180 

4) 

(n − 2) ⋅ 180 

n 

69 If JKL ≅ MNO, which statement is always 

true? 

1) ∠KLJ ≅ ∠NMO 

2) ∠KJL ≅ ∠MON 

3) JL ≅ MO 

4) JK ≅ ON 

70 In the diagram below, m and QR⊥ ST at R. 

If m∠1 = 63, find m∠2. 

71 The coordinates of the endpoints of AB are A(0,0) 

and B(0,6). The equation of the perpendicular 

bisector of AB is 

1) x = 0 

2) x = 3 

3) y = 0 

4) y = 3 

72 In the diagram below of right triangle ABC, CD is 

the altitude to hypotenuse AB, CB = 6, and AD = 5. 

What is the length of BD? 

1) 5 

2) 9 

3) 3 

4) 4


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73 In the diagram below of BCD, side DB is 

extended to point A. 


1) m∠C > m∠D 

2) m∠ABC < m∠D 

3) m∠ABC > m∠C 

4) m∠ABC > m∠C + m∠D 

74 The statement "x is a multiple of 3, and x is an even 

integer" is true when x is equal to 

1) 9 

2) 8 

3) 3 

4) 6 

75 The point (3,−2) is rotated 90º about the origin and 

then dilated by a scale factor of 4. What are the 

coordinates of the resulting image? 

1) (−12,8) 

2) (12,-8) 

3) (8,12) 

4) (−8,−12) 

76 What is the image of the point (−5,2) under the 

translation T 3,−4 ? 

1) (−9,5) 

2) (−8,6) 

3) (−2,−2) 

4) (−15,−8) 

77 Triangle ABC has vertices A(3,3), B(7,9), and 

C(11,3). Determine the point of intersection of the 

medians, and state its coordinates. [The use of the 

set of axes below is optional.] 

78 A sphere has a diameter of 18 meters. Find the 

volume of the sphere, in cubic meters, in terms of 

π . 

79 The Parkside Packing Company needs a 

rectangular shipping box. The box must have a 

length of 11 inches and a width of 8 inches. Find, 

to the nearest tenth of an inch, the minimum height 

of the box such that the volume is at least 800 

cubic inches.


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80 In the diagram below of circle O, diameter AB is 

parallel to chord CD. 

If mCD = 70, what is mAC ? 

1) 110 

2) 70 

3) 55 

4) 35 

81 In the diagram below of circle O, diameter AOB is 

perpendicular to chord CD at point E, OA = 6, and 

OE = 2. 

What is the length of CE? 

1) 4 3 

2) 2 3 

3) 8 2 

4) 4 2 

82 Which diagram represents a correct construction of 

equilateral ABC, given side AB? 

1) 

2) 

3) 

4)


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83 In scalene triangle ABC, m∠B = 45 and m∠C = 55. 

What is the order of the sides in length, from 

longest to shortest? 

1) AB, BC , AC 

2) BC , AC, AB 

3) AC, BC , AB 

4) BC , AB, AC 

84 What is the equation of a line passing through 

(2,−1) and parallel to the line represented by the 

equation y = 2x + 1? 

1) y = − 1 

2 x 

2) y = − 1 

x + 1 

2 

3) y = 2x − 5 

4) y = 2x − 1 

85 In the diagram of quadrilateral ABCD, AB CD, 

∠ABC ≅ ∠CDA, and diagonal AC is drawn. 

Which method can be used to prove ABC is 

congruent to CDA? 

1) AAS 

2) SSA 

3) SAS 

4) SSS 

86 The vertices of parallelogram ABCD are A(2,0), 

B(0,−3), C(3,−3), and D(5,0). If ABCD is 

reflected over the x-axis, how many vertices remain 

invariant? 

1) 1 

2) 2 

3) 3 

4) 0 

87 Line segment AB is shown in the diagram below. 

Which two sets of construction marks, labeled I, II, 

III, and IV, are part of the construction of the 

perpendicular bisector of line segment AB? 

1) I and II 

2) I and III 

3) II and III 

4) II and IV 

88 Lines a and b intersect at point P. Line c passes 

through P and is perpendicular to the plane 

containing lines a and b. Which statement must be 

true? 

1) Lines a, b, and c are coplanar. 

2) Line a is perpendicular to line b. 

3) Line c is perpendicular to both line a and line 

b. 

4) Line c is perpendicular to line a or line b, but 

not both.


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89 In the diagram below, ABC ∼ RST. 

Which statement is not true? 

1) ∠A ≅ ∠R 

2) 

AB BC 

= 

RS ST 

3) 

AB ST 

= 

BC RS 

4) 

AB + BC + AC AB 

= 

RS + ST + RT RS 

90 A pentagon is drawn on the set of axes below. If 

the pentagon is reflected over the y-axis, determine 

if this transformation is an isometry. Justify your 

answer. [The use of the set of axes is optional.] 

91 When a quadrilateral is reflected over the line 

y = x, which geometric relationship is not 

preserved? 

1) congruence 

2) orientation 

3) parallelism 

4) perpendicularity 

92 Which equation represents the line parallel to the 

line whose equation is 4x + 2y = 14 and passing 

through the point (2,2)? 

1) y = −2x 

2) y = −2x + 6 

3) y = 1 

2 x 

4) y = 1 

x + 1 

2 

93 In the diagram below, LMO is isosceles with 

LO = MO. 

If m∠L = 55 and m∠NOM = 28, what is m∠N ? 

1) 27 

2) 28 

3) 42 

4) 70


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94 On the diagram below, use a compass and 

straightedge to construct the bisector of ∠XYZ. 


95 In the diagram below, trapezoid ABCD, with bases 

AB and DC , is inscribed in circle O, with diameter 

DC . If mAB=80, find mBC . 

96 In the diagram below of ABCD, AC ≅ BD. 

Using this information, it could be proven that 

1) BC = AB 

2) AB = CD 

3) AD − BC = CD 

4) AB + CD = AD 

97 In a given triangle, the point of intersection of the 

three medians is the same as the point of 

intersection of the three altitudes. Which 

classification of the triangle is correct? 

1) scalene triangle 

2) isosceles triangle 

3) equilateral triangle 

4) right isosceles triangle 

98 In the diagram below, quadrilateral JUMP is 

inscribed in a circle.. 

Opposite angles J and M must be 

1) right 

2) complementary 

3) congruent 

4) supplementary


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99 Which equation represents a line that is parallel to 

the line whose equation is y = 3 

x − 3 and passes 

2 

through the point (1,2)? 

1) y = 3 1 

x + 

2 2 

2) y = 2 4 

x + 

3 3 

3) y = 3 

x − 2 

2 

4) y = − 2 8 

x + 

3 3 

100 As shown in the diagram below of ABC, a 

compass is used to find points D and E, equidistant 

from point A. Next, the compass is used to find 

point F, equidistant from points D and E. Finally, a 

straightedge is used to draw AF → ⎯⎯ 

. Then, point G, 

the intersection of AF → ⎯⎯ 

and side BC of ABC, is 

labeled. 


1) AF → ⎯⎯ 

⎯⎯ 

2) 

bisects side BC 

AF → 

bisects ∠BAC 

3) AF → ⎯⎯ 

⊥ BC 

4) ABG ∼ ACG 

101 As shown in the diagram below, EF → ←⎯⎯ 

planes P, Q, and R. 

If EF → ←⎯⎯ 

intersects 

is perpendicular to planes P and R, which 

statement must be true? 

1) Plane P is perpendicular to plane Q. 

2) Plane R is perpendicular to plane P. 

3) Plane P is parallel to plane Q. 

4) Plane R is parallel to plane P. 

102 What is an equation of the line that is perpendicular 

to the line whose equation is y = 3 

x − 2 and that 

5 

passes through the point (3,−6)? 

1) y = 5 

x − 11 

3 

2) y = − 5 

x + 11 

3 

3) y = − 5 

x − 1 

3 

4) y = 5 

x + 1 

3 

103 Point A lies in plane B. How many lines can be 

drawn perpendicular to plane B through point A? 

1) one 

2) two 

3) zero 

4) infinite


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104 In the diagram below, PA and PB are tangent to 

circle O, OA and OB are radii, and OP intersects 

the circle at C. Prove: ∠AOP ≅ ∠BOP 

105 The coordinates of the vertices of ABC are 

A(1,2), B(−4,3), and C(−3,−5). State the 

coordinates of A' B' C', the image of ABC after 

a rotation of 90º about the origin. [The use of the 

set of axes below is optional.] 

106 In the diagram below, A′B′C ′ is a transformation 

of ABC, and A″B″C ″ is a transformation of 

A′B′C ′. 

The composite transformation of ABC to 

A″B″C ″ is an example of a 

1) reflection followed by a rotation 

2) reflection followed by a translation 

3) translation followed by a rotation 

4) translation followed by a reflection 

107 What is the length of AB with endpoints A(−1,0) 

and B(4,−3)? 

1) 6 

2) 18 

3) 34 

4) 50


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108 On the set of axes below, graph the locus of points 

that are four units from the point (2,1). On the 

same set of axes, graph the locus of points that are 

two units from the line x = 4. State the coordinates 

of all points that satisfy both conditions. 

109 What is the slope of a line perpendicular to the line 

whose equation is 20x − 2y = 6? 

1) −10 

2) − 1 

10 

3) 10 

4) 

1 

10 

110 The equation of line k is y = 1 

x − 2. The equation 

3 

of line m is −2x + 6y = 18. Lines k and m are 

1) parallel 


3) the same line 

4) neither parallel nor perpendicular 

111 Point P lies on line m. Point P is also included in 

distinct planes Q, R, S, and T. At most, how many 

of these planes could be perpendicular to line m? 

1) 1 

2) 2 

3) 3 

4) 4 

112 The slope of line is − 1 

. What is an equation of a 

3 

line that is perpendicular to line ? 

1) y + 2 = 1 

3 x 

2) −2x + 6 = 6y 

3) 9x − 3y = 27 

4) 3x + y = 0 


the line whose equation is 3x + 5y = 4? 

1) − 3 

5 

2) 

3 

5 

3) − 5 

4) 

5 

3 

3


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114 The coordinates of the vertices of RST are 

R(−2,3), S(4,4), and T(2,−2). Triangle R′S ′T ′ is 

the image of RST after a rotation of 90° about 

the origin. State the coordinates of the vertices of 

R′S ′T ′. [The use of the set of axes below is 

optional.] 

115 In circle O, diameter RS has endpoints 

R(3a,2b − 1) and S(a − 6,4b + 5). Find the 

coordinates of point O, in terms of a and b. 

Express your answer in simplest form. 

116 Determine whether the two lines represented by the 

equations y = 2x + 3 and 2y + x = 6 are parallel, 

perpendicular, or neither. Justify your response. 

117 As shown in the diagram below, FJ is contained in 

plane R, BC and DE are contained in plane S, and 

FJ , BC , and DE intersect at A. 

Which fact is not sufficient to show that planes R 

and S are perpendicular? 

1) FA ⊥ DE 

2) AD ⊥ AF 

3) BC ⊥ FJ 

4) DE ⊥ BC 

118 In the diagram below of ABC, BC is extended to 

D. 

If m∠A = x 2 − 6x, m∠B = 2x − 3, and 

m∠ACD = 9x + 27, what is the value of x? 

1) 10 

2) 2 

3) 3 

4) 15


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119 Triangle HKL has vertices H(−7,2), K(3,−4), and 

L(5,4). The midpoint of HL is M and the midpoint 

of LK is N. Determine and state the coordinates of 

points M and N. Justify the statement: MN is 

parallel to HK. [The use of the set of axes below is 

optional.] 

120 Which quadrilateral has diagonals that always 

bisect its angles and also bisect each other? 

1) rhombus 

2) rectangle 

3) parallelogram 

4) isosceles trapezoid 

121 In the diagram below of ACE, medians AD, EB, 

and CF intersect at G. The length of FG is 12 cm. 

What is the length, in centimeters, of GC? 

1) 24 

2) 12 

3) 6 

4) 4 

122 What is an equation of circle O shown in the graph 

below? 

1) (x + 1) 2 + (y − 3) 2 = 25 

2) (x − 1) 2 + (y + 3) 2 = 25 

3) (x − 5) 2 + (y + 6) 2 = 25 

4) (x + 5) 2 + (y − 6) 2 = 25


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123 Write an equation of the circle graphed in the 

diagram below. 

124 Which set of numbers does not represent the sides 

of a right triangle? 

1) {6,8,10} 

2) {8,15,17} 

3) {8,24,25} 

4) {15,36,39} 

125 The equation of a circle with its center at (−3,5) 

and a radius of 4 is 

1) (x + 3) 2 + (y − 5) 2 = 4 

2) (x − 3) 2 + (y + 5) 2 = 4 

3) (x + 3) 2 + (y − 5) 2 = 16 

4) (x − 3) 2 + (y + 5) 2 = 16 

126 When a dilation is performed on a hexagon, which 

property of the hexagon will not be preserved in its 

image? 

1) parallelism 

2) orientation 

3) length of sides 

4) measure of angles 

127 When solved graphically, what is the solution to 

the following system of equations? 

y = x 2 − 4x + 6 

1) (1,4) 

2) (4,6) 

3) (1,3) and (4,6) 

4) (3,1) and (6,4) 

y = x + 2 

128 As shown on the set of axes below, GHS has 

vertices G(3,1), H(5,3), and S(1,4). Graph and 

state the coordinates of G″H ″S ″, the image of 

GHS after the transformation T −3,1 D 2 .


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129 The diagram below shows the construction of AB → ←⎯ 

through point P parallel to CD → ←⎯⎯ 

. 

Which theorem justifies this method of 

construction? 

1) If two lines in a plane are perpendicular to a 

transversal at different points, then the lines are 

parallel. 

2) If two lines in a plane are cut by a transversal 

to form congruent corresponding angles, then 

the lines are parallel. 


to form congruent alternate interior angles, 

then the lines are parallel. 


to form congruent alternate exterior angles, 

then the lines are parallel. 

130 Parallelogram ABCD has coordinates A(1,5), 

B(6,3), C(3,−1), and D(−2,1). What are the 

coordinates of E, the intersection of diagonals AC 

and BD? 

1) (2,2) 

2) (4.5,1) 

3) (3.5,2) 

4) (−1,3) 

131 A line segment has endpoints (4,7) and (1,11). 

What is the length of the segment? 

1) 5 

2) 7 

3) 16 

4) 25 

132 What are the center and the radius of the circle 

whose equation is (x − 5) 2 + (y + 3) 2 = 16? 

1) (−5,3) and 16 

2) (5,−3) and 16 

3) (−5,3) and 4 

4) (5,−3) and 4 

133 In the diagram below, MATH is a rhombus with 

diagonals AH and MT. 

If m∠HAM = 12, what is m∠AMT ? 

1) 12 

2) 78 

3) 84 

4) 156


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134 In ABC, AB = 5 feet and BC = 3 feet. Which 

inequality represents all possible values for the 

length of AC, in feet? 

1) 2 ≤ AC ≤ 8 

2) 2 < AC < 8 

3) 3 ≤ AC ≤ 7 

4) 3 < AC < 7 

135 As shown in the diagram below, lines m and n are 

cut by transversal p. 

If m∠1 = 4x + 14 and m∠2 = 8x + 10, lines m and n 

are parallel when x equals 

1) 1 

2) 6 

3) 13 

4) 17 

136 Scalene triangle ABC is similar to triangle DEF. 

Which statement is false? 

1) AB :BC =DE:EF 

2) AC :DF =BC :EF 

3) ∠ACB ≅ ∠DFE 

4) ∠ABC ≅ ∠EDF 

137 The diagonals of a quadrilateral are congruent but 

do not bisect each other. This quadrilateral is 

1) an isosceles trapezoid 

2) a parallelogram 

3) a rectangle 

4) a rhombus 

138 Triangle ABC has coordinates A(2,−2), B(2,1), and 

C(4,−2). Triangle A′B′C ′ is the image of ABC 

under T 5,−2 . On the set of axes below, graph and 

label ABC and its image, A′B′C ′. Determine 

the relationship between the area of ABC and the 

area of A′B′C ′. Justify your response. 

139 The angle formed by the radius of a circle and a 

tangent to that circle has a measure of 

1) 45° 

2) 90° 

3) 135° 

4) 180°


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140 What is the equation of a circle whose center is 4 

units above the origin in the coordinate plane and 

whose radius is 6? 

1) x 2 + (y − 6) 2 = 16 

2) (x − 6) 2 + y 2 = 16 

3) x 2 + (y − 4) 2 = 36 

4) (x − 4) 2 + y 2 = 36 

141 A packing carton in the shape of a triangular prism 

is shown in the diagram below. 

What is the volume, in cubic inches, of this carton? 

1) 20 

2) 60 

3) 120 

4) 240 

142 Which compound statement is true? 

1) A triangle has three sides and a quadrilateral 

has five sides. 

2) A triangle has three sides if and only if a 

quadrilateral has five sides. 

3) If a triangle has three sides, then a quadrilateral 

has five sides. 

4) A triangle has three sides or a quadrilateral has 

five sides. 

143 In the diagram below of circle O, diameter AB is 

perpendicular to chord CD at E. If AO = 10 and 

BE = 4, find the length of CE. 

144 What is an equation of the circle shown in the 

graph below? 

1) (x − 3) 2 + (y − 4) 2 = 25 

2) (x + 3) 2 + (y + 4) 2 = 25 

3) (x − 3) 2 + (y − 4) 2 = 10 

4) (x + 3) 2 + (y + 4) 2 = 10


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145 How many points are both 4 units from the origin 

and also 2 units from the line y = 4? 

1) 1 

2) 2 

3) 3 

4) 4 

146 The diameter of a sphere is 15 inches. What is the 

volume of the sphere, to the nearest tenth of a 

cubic inch? 

1) 706.9 

2) 1767.1 

3) 2827.4 

4) 14,137.2 

147 In ABC shown below, P is the centroid and 

BF = 18. 

What is the length of BP ? 

1) 6 

2) 9 

3) 3 

4) 12 

148 As shown in the diagram below, ABC ∼ DEF, 

AB = 7x, BC = 4, DE = 7, and EF = x. 

What is the length of AB? 

1) 28 

2) 2 

3) 14 

4) 4 

149 When writing a geometric proof, which angle 

relationship could be used alone to justify that two 

angles are congruent? 

1) supplementary angles 

2) linear pair of angles 

3) adjacent angles 

4) vertical angles 

150 Find the slope of a line perpendicular to the line 

whose equation is 2y − 6x = 4. 

151 What is the volume, in cubic centimeters, of a 

cylinder that has a height of 15 cm and a diameter 

of 12 cm? 

1) 180π 

2) 540π 

3) 675π 

4) 2,160π


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152 As shown in the diagram below, a kite needs a 

vertical and a horizontal support bar attached at 

opposite corners. The upper edges of the kite are 7 

inches, the side edges are x inches, and the vertical 

support bar is (x + 1) inches. 

What is the measure, in inches, of the vertical 

support bar? 

1) 23 

2) 24 

3) 25 

4) 26 

153 Quadrilateral MNOP is a trapezoid with MN OP. 

If M ′N ′O′P ′ is the image of MNOP after a 

reflection over the x-axis, which two sides of 

quadrilateral M ′N ′O′P ′ are parallel? 

1) M ′N ′ and O′P ′ 

2) M ′N ′ and N ′O′ 

3) P ′M ′ and O′P ′ 

4) P ′M ′ and N ′O′ 

154 If AB → ←⎯ 

is contained in plane P, and AB → ←⎯ 

is 

perpendicular to plane R, which statement is true? 

1) AB → ←⎯ 

is parallel to plane R. 

2) Plane P is parallel to plane R. 

3) AB → ←⎯ 

is perpendicular to plane P. 

4) Plane P is perpendicular to plane R. 

155 The volume, in cubic centimeters, of a sphere 

whose diameter is 6 centimeters is 

1) 12π 

2) 36π 

3) 48π 

4) 288π 

156 In AED with ABCD shown in the diagram 

below, EB and EC are drawn. 

If AB ≅ CD, which statement could always be 

proven? 

1) AC ≅ DB 

2) AE ≅ ED 

3) AB ≅ BC 

4) EC ≅ EA


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157 Triangle TAP has coordinates T(−1,4), A(2,4), and 

P(2,0). On the set of axes below, graph and label 

T ′A′P ′, the image of TAP after the translation 

(x,y) → (x − 5,y − 1). 

158 In parallelogram ABCD shown below, diagonals 

AC and BD intersect at E. 


1) AC ≅ DB 

2) ∠ABD ≅ ∠CBD 

3) AED ≅ CEB 

4) DCE ≅ BCE 

159 The diagram below shows ABC, with AEB, 

ADC, and ∠ACB ≅ ∠AED. Prove that ABC is 

similar to ADE. 

160 Which reason could be used to prove that a 

parallelogram is a rhombus? 

1) Diagonals are congruent. 

2) Opposite sides are parallel. 

3) Diagonals are perpendicular. 

4) Opposite angles are congruent. 

161 In the diagram of ABC shown below, DE BC . 

If AB = 10, AD = 8, and AE = 12, what is the 

length of EC ? 

1) 6 

2) 2 

3) 3 

4) 15


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162 In the diagram below of circle O, chord AB is 

parallel to chord CD. 


1) AC ≅ BD 

2) AB ≅ CD 

3) AB ≅ CD 

4) ABD ≅ CDB 

163 In the diagram below, DE joins the midpoints of 

two sides of ABC. 


1) CE = 1 

2 CB 

2) DE = 1 

2 AB 

3) area of CDE = 1 

area of 

2 

CAB 

4) perimeter of CDE = 1 

perimeter of 

2 

CAB 

164 As shown in the diagram below, the diagonals of 

parallelogram QRST intersect at E. If 

QE = x 2 + 6x, SE = x + 14, and TE = 6x − 1, 

determine TE algebraically. 

165 In the diagram below of isosceles trapezoid ABCD, 

AB = CD = 25, AD = 26, and BC = 12. 

What is the length of an altitude of the trapezoid? 

1) 7 

2) 14 

3) 19 

4) 24 

166 Plane R is perpendicular to line k and plane D is 

perpendicular to line k. Which statement is 

correct? 

1) Plane R is perpendicular to plane D. 

2) Plane R is parallel to plane D. 

3) Plane R intersects plane D. 

4) Plane R bisects plane D.


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167 Given: ABC with vertices A(−6,−2), B(2,8), and 

C(6,−2). AB has midpoint D, BC has midpoint E, 

and AC has midpoint F. 

Prove: ADEF is a parallelogram 

ADEF is not a rhombus 

[The use of the grid is optional.] 

168 A circle has the equation (x − 2) 2 + (y + 3) 2 = 36. 

What are the coordinates of its center and the 

length of its radius? 

1) (−2,3) and 6 

2) (2,−3) and 6 

3) (−2,3) and 36 

4) (2,−3) and 36 

169 Triangle PQR has angles in the ratio of 2:3:5. 

Which type of triangle is PQR? 

1) acute 

2) isosceles 

3) obtuse 

4) right 

170 In the diagram of KLM below, m∠L = 70, 

m∠M = 50, and MK is extended through N. 

What is the measure of ∠LKN ? 

1) 60º 

2) 120º 

3) 180º 

4) 300º 

171 The diagram below shows a pair of congruent 

triangles, with ∠ADB ≅ ∠CDB and 

∠ABD ≅ ∠CBD. 


1) ∠ADB ≅ ∠CBD 

2) ∠ABC ≅ ∠ADC 

3) AB ≅ CD 

4) AD ≅ CD


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172 The graph below shows JT and its image, J ′T ′, 

after a transformation. 

Which transformation would map JT onto J ′T ′? 



3) rotation centered at the origin 

4) reflection through the origin 

173 In circle O shown below, diameter DB is 

perpendicular to chord AC at E. 

If DB = 34, AC = 30, and DE > BE, what is the 

length of BE? 

1) 8 

2) 9 

3) 16 

4) 25 

174 In PQR, ∠PRQ is a right angle and RT is drawn 

perpendicular to hypotenuse PQ. If PT = x, 

RT = 6, and TQ = 4x, what is the length of PQ? 

1) 9 

2) 12 

3) 3 

4) 15 

175 In the diagram below, tangent ML and secant MNK 

are drawn to circle O. The ratio 

mLN : mNK : mKL is 3:4:5. Find m∠LMK . 

176 What is the length of the line segment whose 

endpoints are A(−1,9) and B(7,4)? 

1) 61 

2) 89 

3) 205 

4) 233


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177 Which type of triangle can be drawn using the 

points (−2,3), (−2,−7), and (4,−5)? 

1) scalene 

2) isosceles 

3) equilateral 

4) no triangle can be drawn 

178 The diagram below represents a rectangular solid. 


1) EH and BC are coplanar 

2) FG and AB are coplanar 

3) EH and AD are skew 

4) FG and CG are skew 

179 In the diagram below, two parallel lines intersect 

circle O at points A, B, C, and D, with 

mAB = x + 20 and mDC = 2x − 20. Find mAB. 

180 In the diagram below, point P is the centroid of 

ABC. 

If PM = 2x + 5 and BP = 7x + 4, what is the length 

of PM ? 

1) 9 

2) 2 

3) 18 

4) 27 

181 In the diagram below, EF is the median of 

trapezoid ABCD. 

If AB = 5x − 9, DC = x + 3, and EF = 2x + 2, what 

is the value of x? 

1) 5 

2) 2 

3) 7 

4) 8


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182 Given: AD bisects BC at E. 

AB⊥ BC 

DC ⊥ BC 

Prove: AB ≅ DC 

183 In the diagram of ABC shown below, D is the 

midpoint of AB, E is the midpoint of BC , and F is 

the midpoint of AC. 

If AB = 20, BC = 12, and AC = 16, what is the 

perimeter of trapezoid ABEF? 

1) 24 

2) 36 

3) 40 

4) 44 

184 On the set of axes below, graph the locus of points 

that are 4 units from the line x = 3 and the locus of 

points that are 5 units from the point (0,2). Label 

with an X all points that satisfy both conditions. 

185 As shown in the diagram of ACD below, B is a 

point on AC and DB is drawn. 

If m∠A = 66, m∠CDB = 18, and m∠C = 24, what 

is the longest side of ABD? 

1) AB 

2) DC 

3) AD 

4) BD


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186 In the diagram below of ABC, AB ≅ AC, 

m∠A = 3x, and m∠B = x + 20. 

What is the value of x? 

1) 10 

2) 28 

3) 32 

4) 40 

187 Lines m and n intersect at point A. Line k is 

perpendicular to both lines m and n at point A. 


1) Lines m, n, and k are in the same plane. 

2) Lines m and n are in two different planes. 

3) Lines m and n are perpendicular to each other. 

4) Line k is perpendicular to the plane containing 

lines m and n. 

188 What is the length of the line segment whose 

endpoints are (1,−4) and (9,2)? 

1) 5 

2) 2 17 

3) 10 

4) 2 26 

189 Given the true statement, "The medians of a 

triangle are concurrent," write the negation of the 

statement and give the truth value for the negation. 

190 In the diagram below of rhombus ABCD, 

m∠C = 100. 

What is m∠DBC ? 

1) 40 

2) 45 

3) 50 

4) 80 

191 Which equation represents the line that is 

perpendicular to 2y = x + 2 and passes through the 

point (4,3)? 

1) y = 1 

x − 5 

2 

2) y = 1 

x + 1 

2 

3) y = −2x + 11 

4) y = −2x − 5 

192 Two lines are represented by the equations 

x + 2y = 4 and 4y − 2x = 12. Determine whether 

these lines are parallel, perpendicular, or neither. 

Justify your answer.


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193 An equation of the line that passes through (2,−1) 

and is parallel to the line 2y + 3x = 8 is 

1) y = 3 

x − 4 

2 

2) y = 3 

x + 4 

2 

3) y = − 3 

x − 2 

2 

4) y = − 3 

x + 2 

2 

194 In the diagram below of PAO, AP is tangent to 

circle O at point A, OB = 7, and BP = 18. 

What is the length of AP? 

1) 10 

2) 12 

3) 17 

4) 24 

195 In rhombus ABCD, the diagonals AC and BD 

intersect at E. If AE = 5 and BE = 12, what is the 

length of AB? 

1) 7 

2) 10 

3) 13 

4) 17 

196 In the diagram below of circle O, chords AB and 

CD intersect at E. 

If m∠AEC = 34 and mAC = 50, what is mDB ? 

1) 16 

2) 18 

3) 68 

4) 118 

197 Which equation of a circle will have a graph that 

lies entirely in the first quadrant? 

1) (x − 4) 2 + (y − 5) 2 = 9 

2) (x + 4) 2 + (y + 5) 2 = 9 

3) (x + 4) 2 + (y + 5) 2 = 25 

4) (x − 5) 2 + (y − 4) 2 = 25 

198 In RST, m∠R = 58 and m∠S = 73. Which 

inequality is true? 

1) RT < TS < RS 

2) RS < RT < TS 

3) RT < RS < TS 

4) RS < TS < RT


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199 Line n intersects lines l and m, forming the angles 

shown in the diagram below. 

Which value of x would prove l m? 

1) 2.5 

2) 4.5 

3) 6.25 

4) 8.75 

200 The vertices of RST are R(−6,5), S(−7,−2), and 

T(1,4). The image of RST after the composition 

T−2,3 r y = x is R"S"T". State the coordinates of 

R"S"T". [The use of the set of axes below is 

optional.] 

201 Quadrilateral MATH has coordinates M(1,1), 

A(−2,5), T(3,5), and H(6,1). Prove that 

quadrilateral MATH is a rhombus and prove that it 

is not a square. [The use of the grid is optional.] 

202 In the diagram below of circle O, PA is tangent to 

circle O at A, and PBC is a secant with points B 

and C on the circle. 

If PA = 8 and PB = 4, what is the length of BC ? 

1) 20 

2) 16 

3) 15 

4) 12


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203 In the diagram below of right triangle ABC, altitude 

BD is drawn to hypotenuse AC, AC = 16, and 

CD = 7. 


1) 3 7 

2) 4 7 

3) 7 3 

4) 12 

204 Triangle ABC is graphed on the set of axes below. 

Which transformation produces an image that is 

similar to, but not congruent to, ABC? 

1) T2,3 2) D 2 

3) r y = x 

4) R 90 

205 In the diagram below of circle O, chord AB bisects 

chord CD at E. If AE = 8 and BE = 9, find the 

length of CE in simplest radical form. 

206 What is an equation of circle O shown in the graph 

below? 

1) (x + 2) 2 + (y − 2) 2 = 9 

2) (x + 2) 2 + (y − 2) 2 = 3 

3) (x − 2) 2 + (y + 2) 2 = 9 

4) (x − 2) 2 + (y + 2) 2 = 3


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207 In the diagram below, ABC is circumscribed 

about circle O and the sides of ABC are tangent 

to the circle at points D, E, and F. 

If AB = 20, AE = 12, and CF = 15, what is the 

length of AC? 

1) 8 

2) 15 

3) 23 

4) 27 

208 In the diagram of JEA below, m∠JEA = 90 and 

m∠EAJ = 48. Line segment MS connects points M 

and S on the triangle, such that m∠EMS = 59. 

What is m∠JSM ? 

1) 163 

2) 121 

3) 42 

4) 17 

209 What is an equation of a circle with center (7,−3) 

and radius 4? 

1) (x − 7) 2 + (y + 3) 2 = 4 

2) (x + 7) 2 + (y − 3) 2 = 4 

3) (x − 7) 2 + (y + 3) 2 = 16 

4) (x + 7) 2 + (y − 3) 2 = 16 

210 In the diagram below of DAE and BCE, AB 

and CD intersect at E, such that AE ≅ CE and 

∠BCE ≅ ∠DAE. 

Triangle DAE can be proved congruent to triangle 

BCE by 

1) ASA 

2) SAS 

3) SSS 

4) HL 

211 If the vertex angles of two isosceles triangles are 

congruent, then the triangles must be 

1) acute 

2) congruent 

3) right 

4) similar


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212 In the diagram below of ABC, TV → ←⎯ 

BC , AT = 5, 

TB = 7, and AV = 10. 

What is the length of VC? 

1) 3 1 

2 

2) 7 1 

7 

3) 14 

4) 24 

213 The two lines represented by the equations below 

are graphed on a coordinate plane. 

x + 6y = 12 

3(x − 2) = −y − 4 

Which statement best describes the two lines? 

1) The lines are parallel. 

2) The lines are the same line. 

3) The lines are perpendicular. 

4) The lines intersect at an angle other than 90°. 

214 What is an equation of the circle with a radius of 5 

and center at (1,−4)? 

1) (x + 1) 2 + (y − 4) 2 = 5 

2) (x − 1) 2 + (y + 4) 2 = 5 

3) (x + 1) 2 + (y − 4) 2 = 25 

4) (x − 1) 2 + (y + 4) 2 = 25 

215 On the set of axes below, solve the system of 

equations graphically and state the coordinates of 

all points in the solution. 

y = (x − 2) 2 − 3 

2y + 16 = 4x 

216 In the diagram below, AB, BC , and AC are 

tangents to circle O at points F, E, and D, 

respectively, AF = 6, CD = 5, and BE = 4. 

What is the perimeter of ABC? 

1) 15 

2) 25 

3) 30 

4) 60


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217 The vertices of the triangle in the diagram below 

are A(7,9), B(3,3), and C(11,3). 

What are the coordinates of the centroid of 

ABC? 

1) (5,6) 

2) (7,3) 

3) (7,5) 

4) (9,6) 

218 In the diagram below, lines n and m are cut by 

transversals p and q. 

What value of x would make lines n and m parallel? 

1) 110 

2) 80 

3) 70 

4) 50 

219 On the set of axes below, solve the following 

system of equations graphically and state the 

coordinates of all points in the solution. 

(x + 3) 2 + (y − 2) 2 = 25 

2y + 4 = −x 


C(0,4). The triangle may be classified as 

1) equilateral 

2) isosceles 

3) right 

4) scalene 

221 A sphere is inscribed inside a cube with edges of 6 

cm. In cubic centimeters, what is the volume of the 

sphere, in terms of π? 

1) 12π 

2) 36π 

3) 48π 

4) 288π


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222 The number of degrees in the sum of the interior 

angles of a pentagon is 

1) 72 

2) 360 

3) 540 

4) 720 

223 The graph below shows the locus of points 

equidistant from the x-axis and y-axis. On the same 

set of axes, graph the locus of points 3 units from 

the line x = 0. Label with an X all points that 

satisfy both conditions. 

224 A cylinder has a height of 7 cm and a base with a 

diameter of 10 cm. Determine the volume, in cubic 

centimeters, of the cylinder in terms of π . 

225 When ABC is dilated by a scale factor of 2, its 

image is A′B′C ′. Which statement is true? 

1) AC ≅ A′C ′ 

2) ∠A ≅ ∠A′ 

3) perimeter of ABC = perimeter of A′B′C ′ 

4) 2(area of ABC) = area of A′B′C ′ 

226 In the diagram below of circle O, chords RT and 

QS intersect at M. Secant PTR and tangent PS are 

drawn to circle O. The length of RM is two more 

than the length of TM , QM = 2, SM = 12, and 

PT = 8. 

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 

tangents drawn to them from external point T. The 

points of tangency are C, A, S, and E. The ratio of 

TA to AC is 1:3. If TS = 24, find the length of SE. 

228 In ABC, m∠A = x, m∠B = 2x + 2, and 

m∠C = 3x + 4. What is the value of x? 

1) 29 

2) 31 

3) 59 

4) 61 

229 Lines j and k intersect at point P. Line m is drawn 

so that it is perpendicular to lines j and k at point P. 

Which statement is correct? 

1) Lines j and k are in perpendicular planes. 

2) Line m is in the same plane as lines j and k. 

3) Line m is parallel to the plane containing lines j 

and k. 

4) Line m is perpendicular to the plane containing 

lines j and k. 

230 In the diagram of ABC and EDC below, AE 

and BD intersect at C, and ∠CAB ≅ ∠CED. 

Which method can be used to show that ABC 

must be similar to EDC? 

1) SAS 

2) AA 

3) SSS 

4) HL 

231 On the grid below, graph the points that are 

equidistant from both the x and y axes and the 

points that are 5 units from the origin. Label with 

an X all points that satisfy both conditions.


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232 Write a statement that is logically equivalent to the 

statement “If two sides of a triangle are congruent, 

the angles opposite those sides are congruent.” 

Identify the new statement as the converse, inverse, 

or contrapositive of the original statement. 


the point (−2,5) and is perpendicular to the line 

whose equation is y = 1 

x + 5? 

1) y = 2x + 1 

2) y = −2x + 1 

3) y = 2x + 9 

4) y = −2x − 9 

234 The lateral faces of a regular pyramid are 

composed of 

1) squares 

2) rectangles 

3) congruent right triangles 

4) congruent isosceles triangles 

235 What is the equation of a line that passes through 

the point (−3,−11) and is parallel to the line whose 

equation is 2x − y = 4? 

1) y = 2x + 5 

2) y = 2x − 5 

3) y = 1 25 

x + 

2 2 

4) y = − 1 25 

x − 

2 2 

236 In RST, m∠RST = 46 and RS ≅ ST. Find 

m∠STR. 

2 

237 In the diagram below, ABC ≅ XYZ. 

Which two statements identify corresponding 

congruent parts for these triangles? 

1) AB ≅ XY and ∠C ≅ ∠Y 

2) AB ≅ YZ and ∠C ≅ ∠X 

3) BC ≅ XY and ∠A ≅ ∠Y 

4) BC ≅ YZ and ∠A ≅ ∠X 

238 Find an equation of the line passing through the 

point (5,4) and parallel to the line whose equation 

is 2x + y = 3. 

239 In the diagram below of circle O, chords AE and 

DC intersect at point B, such that mAC = 36 and 

mDE = 20. 

What is m∠ABC ? 

1) 56 

2) 36 

3) 28 

4) 8


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240 In the diagram below, car A is parked 7 miles from 

car B. Sketch the points that are 4 miles from car A 

and sketch the points that are 4 miles from car B. 

Label with an X all points that satisfy both 

conditions. 

241 What is an equation of a circle with its center at 

(−3,5) and a radius of 4? 

1) (x − 3) 2 + (y + 5) 2 = 16 

2) (x + 3) 2 + (y − 5) 2 = 16 

3) (x − 3) 2 + (y + 5) 2 = 4 

4) (x + 3) 2 + (y − 5) 2 = 4 

242 What are the center and radius of a circle whose 

equation is (x − A) 2 + (y − B) 2 = C? 

1) center = (A,B); radius = C 

2) center = (−A,−B); radius = C 

3) center = (A,B); radius = C 

4) center = (−A,−B); radius = C 

243 What is the measure of an interior angle of a 

regular octagon? 

1) 45º 

2) 60º 

3) 120º 

4) 135º 

244 If a line segment has endpoints A(3x + 5,3y) and 

B(x − 1,−y), what are the coordinates of the 

midpoint of AB? 

1) (x + 3,2y) 

2) (2x + 2,y) 

3) (2x + 3,y) 

4) (4x + 4,2y) 

245 The vertices of ABC are A(3,2), B(6,1), and 

C(4,6). Identify and graph a transformation of 

ABC such that its image, A′B′C ′, results in 

AB A′B′.


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246 Given: ABC and EDC, C is the midpoint of 

BD and AE 

Prove: AB DE 

247 In the diagram below of AGE and OLD, 

∠GAE ≅ ∠LOD, and AE ≅ OD. 

To prove that AGE and OLD are congruent by 

SAS, what other information is needed? 

1) GE ≅ LD 

2) AG ≅ OL 

3) ∠AGE ≅ ∠OLD 

4) ∠AEG ≅ ∠ODL 

248 What is the solution of the following system of 

equations? 

y = (x + 3) 2 − 4 

y = 2x + 5 

1) (0,−4) 

2) (−4,0) 

3) (−4,−3) and (0,5) 

4) (−3,−4) and (5,0) 

249 Which expression best describes the transformation 

shown in the diagram below? 

1) same orientation; reflection 

2) opposite orientation; reflection 

3) same orientation; translation 

4) opposite orientation; translation 

250 Which transformation can map the letter S onto 

itself? 





251 In KLM , m∠K = 36 and KM = 5. The 

transformation D 2 is performed on KLM to form 

K ′L′M ′. Find m∠K ′. Justify your answer. 

Find the length of K ′M ′. Justify your answer.


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252 The coordinates of the vertices of ABC A(1,3), 

B(−2,2) and C(0,−2). On the grid below, graph 

and label A″B″C ″, the result of the composite 

transformation D 2 T 3,−2 . State the coordinates of 

A″, B″, and C ″. 

253 In the diagram below, which transformation was 

used to map ABC to A′B′C ′? 

1) dilation 


3) reflection 


254 Write an equation of the perpendicular bisector of 

the line segment whose endpoints are (−1,1) and 

(7,−5). [The use of the grid below is optional] 

255 In the diagram below of ABC, DE is a 

midsegment of ABC, DE = 7, AB = 10, and 

BC = 13. Find the perimeter of ABC. 

256 In right DEF, m∠D = 90 and m∠F is 12 degrees 

less than twice m∠E . Find m∠E .


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257 Given: Two is an even integer or three is an even 

integer. 

Determine the truth value of this disjunction. 

Justify your answer. 

258 In the diagram below of circle C, mQT = 140, and 

m∠P = 40. 

What is mRS ? 

1) 50 

2) 60 

3) 90 

4) 110 


whose equation is y = − 2 

x − 5? 

3 

1) − 3 

2 

2) − 2 

3 

3) 

2 

3 

4) 

3 

2 

260 On the set of axes below, graph and label DEF 

with vertices at D(−4,−4), E(−2,2), and F(8,−2). If 

G is the midpoint of EF and H is the midpoint of 

DF, state the coordinates of G and H and label 

each point on your graph. Explain why GH DE. 

261 In the diagram below of right triangle ACB, altitude 

CD is drawn to hypotenuse AB. 

If AB = 36 and AC = 12, what is the length of AD? 

1) 32 

2) 6 

3) 3 

4) 4


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262 The diagram below shows the construction of the 

center of the circle circumscribed about ABC. 

This construction represents how to find the 

intersection of 

1) the angle bisectors of ABC 

2) the medians to the sides of ABC 

3) the altitudes to the sides of ABC 

4) the perpendicular bisectors of the sides of 

ABC 

263 In the diagram of circle O below, chords AB and 

CD are parallel, and BD is a diameter of the circle. 

If mAD = 60, what is m∠CDB? 

1) 20 

2) 30 

3) 60 

4) 120 

264 In the diagram below, circle O has a radius of 5, 

and CE = 2. Diameter AC is perpendicular to 

chord BD at E. 


1) 12 

2) 10 

3) 8 

4) 4 

265 In the diagram below of circle O, 

chord AB chord CD, and chord CD chord EF . 


1) CE ≅ DF 

2) AC ≅ DF 

3) AC ≅ CE 

4) EF ≅ CD


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266 In a coordinate plane, how many points are both 5 

units from the origin and 2 units from the x-axis? 

1) 1 

2) 2 

3) 3 

4) 4 

267 In the diagram below, line k is perpendicular to 

plane P at point T. 

Which statement is true? 

1) Any point in plane P also will be on line k. 

2) Only one line in plane P will intersect line k. 

3) All planes that intersect plane P will pass 

through T. 

4) Any plane containing line k is perpendicular to 

plane P. 

268 What is the inverse of the statement “If two 

triangles are not similar, their corresponding angles 

are not congruent”? 

1) If two triangles are similar, their corresponding 

angles are not congruent. 

2) If corresponding angles of two triangles are not 

congruent, the triangles are not similar. 

3) If two triangles are similar, their corresponding 

angles are congruent. 

4) If corresponding angles of two triangles are 

congruent, the triangles are similar. 

269 In the diagram below of ACT, D is the midpoint 

of AC, O is the midpoint of AT, and G is the 

midpoint of CT. 

If AC = 10, AT = 18, and CT = 22, what is the 

perimeter of parallelogram CDOG? 

1) 21 

2) 25 

3) 32 

4) 40 

270 Which geometric principle is used to justify the 

construction below? 

1) A line perpendicular to one of two parallel 

lines is perpendicular to the other. 

2) Two lines are perpendicular if they intersect to 

form congruent adjacent angles. 

3) When two lines are intersected by a transversal 

and alternate interior angles are congruent, the 

lines are parallel. 

4) When two lines are intersected by a transversal 

and the corresponding angles are congruent, the 

lines are parallel.


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271 In the diagram below, RST is a 3 − 4 − 5 right 

triangle. The altitude, h, to the hypotenuse has 

been drawn. Determine the length of h. 

272 On the set of axes below, sketch the points that are 

5 units from the origin and sketch the points that 

are 2 units from the line y = 3. Label with an X all 

points that satisfy both conditions. 

273 Using a compass and straightedge, and AB below, 

construct an equilateral triangle with all sides 

congruent to AB. [Leave all construction marks.] 

274 A quadrilateral whose diagonals bisect each other 

and are perpendicular is a 

1) rhombus 

2) rectangle 

3) trapezoid 

4) parallelogram 

275 In the diagram below of circle O, chords AD and 

BC intersect at E, mAC = 87, and mBD = 35. 

What is the degree measure of ∠CEA? 

1) 87 

2) 61 

3) 43.5 

4) 26


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276 Lines k 1 and k 2 intersect at point E. Line m is 

perpendicular to lines k 1 and k 2 at point E. 

Which statement is always true? 

1) Lines k 1 and k 2 are perpendicular. 

2) Line m is parallel to the plane determined by 

lines k 1 and k 2 . 

3) Line m is perpendicular to the plane 

determined by lines k 1 and k 2 . 

4) Line m is coplanar with lines k 1 and k 2 . 

277 In ABC, AB ≅ BC . An altitude is drawn from B 

to AC and intersects AC at D. Which conclusion is 

not always true? 

1) ∠ABD ≅ ∠CBD 

2) ∠BDA ≅ ∠BDC 

3) AD ≅ BD 

4) AD ≅ DC 

278 A right circular cylinder has a volume of 1,000 

cubic inches and a height of 8 inches. What is the 

radius of the cylinder to the nearest tenth of an 

inch? 

1) 6.3 

2) 11.2 

3) 19.8 

4) 39.8 

279 The diagram below shows a right pentagonal prism. 

Which statement is always true? 

1) BC ED 

2) FG CD 

3) FJ IH 

4) GB HC


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280 The diagram below shows isosceles trapezoid 

ABCD with AB DC and AD ≅ BC . If 

m∠BAD = 2x and m∠BCD = 3x + 5, find m∠BAD. 

281 Triangle ABC has coordinates A(−6,2), B(−3,6), 

and C(5,0). Find the perimeter of the triangle. 

Express your answer in simplest radical form. [The 

use of the grid below is optional.] 

282 Which statement is logically equivalent to "If it is 

warm, then I go swimming" 

1) If I go swimming, then it is warm. 

2) If it is warm, then I do not go swimming. 

3) If I do not go swimming, then it is not warm. 

4) If it is not warm, then I do not go swimming. 

283 In the diagram below of circle O, chords AD and 

BC intersect at E. 

Which relationship must be true? 

1) CAE ≅ DBE 

2) AEC ∼ BED 

3) ∠ACB ≅ ∠CBD 

4) CA ≅ DB 

284 Given ABC with base AFEDC, median BF , 

altitude BD, and BE bisects ∠ABC, which 

conclusion is valid? 

1) ∠FAB ≅ ∠ABF 

2) ∠ABF ≅ ∠CBD 

3) CE ≅ EA 

4) CF ≅ FA


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285 In the diagram below, quadrilateral STAR is a 

rhombus with diagonals SA and TR intersecting at 

E. ST = 3x + 30, SR = 8x − 5, SE = 3z, TE = 5z + 5, 

AE = 4z − 8, m∠RTA = 5y − 2, and 

m∠TAS = 9y + 8. Find SR, RT, and m∠TAS . 

286 Based on the construction below, which statement 

must be true? 

1) m∠ABD = 1 

2 m∠CBD 

2) m∠ABD = m∠CBD 

3) m∠ABD = m∠ABC 

4) m∠CBD = 1 

2 m∠ABD 

287 Line k is drawn so that it is perpendicular to two 

distinct planes, P and R. What must be true about 

planes P and R? 

1) Planes P and R are skew. 

2) Planes P and R are parallel. 

3) Planes P and R are perpendicular. 

4) Plane P intersects plane R but is not 

perpendicular to plane R. 

288 Write an equation of the line that passes through 

the point (6,−5) and is parallel to the line whose 

equation is 2x − 3y = 11. 

289 Tim has a rectangular prism with a length of 10 

centimeters, a width of 2 centimeters, and an 

unknown height. He needs to build another 

rectangular prism with a length of 5 centimeters 

and the same height as the original prism. The 

volume of the two prisms will be the same. Find 

the width, in centimeters, of the new prism. 

290 If two different lines are perpendicular to the same 

plane, they are 

1) collinear 

2) coplanar 

3) congruent 

4) consecutive


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291 Triangle XYZ, shown in the diagram below, is 

reflected over the line x = 2. State the coordinates 

of X ′Y ′Z′, the image of XYZ. 

292 A right circular cone has a base with a radius of 15 

cm, a vertical height of 20 cm, and a slant height of 

25 cm. Find, in terms of' π , the number of square 

centimeters in the lateral area of the cone. 

293 Given the system of equations: y = x 2 − 4x 

x = 4 

The number of points of intersection is 

1) 1 

2) 2 

3) 3 

4) 0 

294 In the diagram below, quadrilateral ABCD is 

inscribed in circle O, AB DC , and diagonals AC 

and BD are drawn. Prove that ACD ≅ BDC. 

295 Tim is going to paint a wooden sphere that has a 

diameter of 12 inches. Find the surface area of the 

sphere, to the nearest square inch. 

296 Through a given point, P, on a plane, how many 

lines can be drawn that are perpendicular to that 

plane? 

1) 1 

2) 2 

3) more than 2 

4) none


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297 In the diagram below of HQP, side HP is 

extended through P to T, m∠QPT = 6x + 20, 

m∠HQP = x + 40, and m∠PHQ = 4x − 5. Find 

m∠QPT . 

298 In the diagram below of quadrilateral ABCD with 

diagonal BD, m∠A = 93, m∠ADB = 43, 

m∠C = 3x + 5, m∠BDC = x + 19, and 

m∠DBC = 2x + 6. Determine if AB is parallel to 

DC . Explain your reasoning. 

299 In the diagram below of parallelogram STUV, 

SV = x + 3, VU = 2x − 1, and TU = 4x − 3. 

What is the length of SV? 

1) 5 

2) 2 

3) 7 

4) 4 

300 In the diagram below, tangent PA and secant PBC 

are drawn to circle O from external point P. 

If PB = 4 and BC = 5, what is the length of PA? 

1) 20 

2) 9 

3) 8 

4) 6


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301 The coordinates of the vertices of parallelogram 

ABCD are A(−2,2), B(3,5), C(4,2), and D(−1,−1). 

State the coordinates of the vertices of 

parallelogram A″B″C ″D″ that result from the 

transformation r y − axis T 2,−3 . [The use of the set of 

axes below is optional. ] 

302 What are the center and the radius of the circle 

whose equation is (x − 3) 2 + (y + 3) 2 = 36 

1) center = (3,−3); radius = 6 

2) center = (−3,3); radius = 6 

3) center = (3,−3); radius = 36 

4) center = (−3,3); radius = 36 

303 If ABC ∼ ZXY, m∠A = 50, and m∠C = 30, 

what is m∠X ? 

1) 30 

2) 50 

3) 80 

4) 100 

304 Two triangles are similar, and the ratio of each pair 

of corresponding sides is 2:1. Which statement 

regarding the two triangles is not true? 

1) Their areas have a ratio of 4:1. 

2) Their altitudes have a ratio of 2:1. 

3) Their perimeters have a ratio of 2:1. 

4) Their corresponding angles have a ratio of 2:1. 

305 The coordinates of the vertices of parallelogram 

ABCD are A(−3,2), B(−2,−1), C(4,1), and D(3,4). 

The slopes of which line segments could be 

calculated to show that ABCD is a rectangle? 

1) AB and DC 

2) AB and BC 

3) AD and BC 

4) AC and BD 

306 In isosceles triangle ABC, AB = BC. Which 

statement will always be true? 

1) m∠B = m∠A 

2) m∠A > m∠B 

3) m∠A = m∠C 

4) m∠C < m∠B 

307 Line segment AB has endpoints A(2,−3) and 

B(−4,6). What are the coordinates of the midpoint 

of AB? 

1) (−2,3) 

2) −1,1 1 

 

2 

3) (−1,3) 

4) 3,4 1 

 

2


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308 Which transformation is not always an isometry? 



3) reflection 


309 On the set of axes below, Geoff drew rectangle 

ABCD. He will transform the rectangle by using 

the translation (x,y) → (x + 2,y + 1) and then will 

reflect the translated rectangle over the x-axis. 

What will be the area of the rectangle after these 

transformations? 

1) exactly 28 square units 

2) less than 28 square units 

3) greater than 28 square units 

4) It cannot be determined from the information 

given. 

310 What is the negation of the statement “Squares are 

parallelograms”? 

1) Parallelograms are squares. 

2) Parallelograms are not squares. 

3) It is not the case that squares are 

parallelograms. 

4) It is not the case that parallelograms are 

squares. 

311 The pentagon in the diagram below is formed by 

five rays. 

What is the degree measure of angle x? 

1) 72 

2) 96 

3) 108 

4) 112 

312 In the diagram below of ACT, BE → ←⎯⎯ 

AT. 

If CB = 3, CA = 10, and CE = 6, what is the length 

of ET ? 

1) 5 

2) 14 

3) 20 

4) 26


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313 The equation of a circle is (x − 2) 2 + (y + 4) 2 = 4. 

Which diagram is the graph of the circle? 

1) 

2) 

3) 

4) 

314 In the diagram below of circle O, secant AB 

intersects circle O at D, secant AOC intersects 

circle O at E, AE = 4, AB = 12, and DB = 6. 

What is the length of OC? 

1) 4.5 

2) 7 

3) 9 

4) 14 

315 In the diagram below of ABC, medians AD, BE , 

and CF intersect at G. 

If CF = 24, what is the length of FG? 

1) 8 

2) 10 

3) 12 

4) 16


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316 Given: Quadrilateral ABCD has vertices A(−5,6), 

B(6,6), C(8,−3), and D(−3,−3). 

Prove: Quadrilateral ABCD is a parallelogram but 

is neither a rhombus nor a rectangle. [The use of 

the grid below is optional.] 

317 A right circular cylinder has an altitude of 11 feet 

and a radius of 5 feet. What is the lateral area, in 

square feet, of the cylinder, to the nearest tenth? 

1) 172.7 

2) 172.8 

3) 345.4 

4) 345.6 

318 The endpoints of CD are C(−2,−4) and D(6,2). 

What are the coordinates of the midpoint of CD? 

1) (2,3) 

2) (2,−1) 

3) (4,−2) 

4) (4,3) 

319 In an equilateral triangle, what is the difference 

between the sum of the exterior angles and the sum 

of the interior angles? 

1) 180° 

2) 120° 

3) 90° 

4) 60° 

320 Using a compass and straightedge, construct a line 

that passes through point P and is perpendicular to 

line m. [Leave all construction marks.] 

321 How many common tangent lines can be drawn to 

the two externally tangent circles shown below? 

1) 1 

2) 2 

3) 3 

4) 4


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322 What is the image of point A(4,2) after the 

composition of transformations defined by 

R 90° r y = x ? 

1) (−4,2) 

2) (4,−2) 

3) (−4,−2) 

4) (2,−4) 

323 The rectangle ABCD shown in the diagram below 

will be reflected across the x-axis. 

What will not be preserved? 

1) slope of AB 

2) parallelism of AB and CD 

3) length of AB 

4) measure of ∠A 

324 If the surface area of a sphere is represented by 

144π , what is the volume in terms of π ? 

1) 36π 

2) 48π 

3) 216π 

4) 288π 

325 Given: Quadrilateral ABCD, diagonal AFEC, 

AE ≅ FC , BF ⊥ AC, DE ⊥ AC, ∠1 ≅ ∠2 

Prove: ABCD is a parallelogram. 

326 The lines 3y + 1 = 6x + 4 and 2y + 1 = x − 9 are 

1) parallel 




327 In the diagram below of circle O, chords AB and 

CD intersect at E. 

If CE = 10, ED = 6, and AE = 4, what is the length 

of EB? 

1) 15 

2) 12 

3) 6.7 

4) 2.4


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328 In the diagram below of regular pentagon ABCDE, 

EB is drawn. 

What is the measure of ∠AEB? 

1) 36º 

2) 54º 

3) 72º 

4) 108º 

329 A regular pyramid with a square base is shown in 

the diagram below. 

A side, s, of the base of the pyramid is 12 meters, 

and the height, h, is 42 meters. What is the volume 

of the pyramid in cubic meters? 

330 The endpoints of PQ are P(−3,1) and Q(4,25). 

Find the length of PQ. 

331 A transversal intersects two lines. Which condition 

would always make the two lines parallel? 

1) Vertical angles are congruent. 

2) Alternate interior angles are congruent. 

3) Corresponding angles are supplementary. 

4) Same-side interior angles are complementary. 

332 What is the negation of the statement “I am not 

going to eat ice cream”? 

1) I like ice cream. 

2) I am going to eat ice cream. 

3) If I eat ice cream, then I like ice cream. 

4) If I don’t like ice cream, then I don’t eat ice 

cream. 

333 In the diagram below of ADB, m∠BDA = 90, 

AD = 5 2, and AB = 2 15. 


1) 10 

2) 20 

3) 50 

4) 110


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334 What is the distance between the points (−3,2) and 

(1,0)? 

1) 2 2 

2) 2 3 

3) 5 2 

4) 2 5 

335 What is the contrapositive of the statement, “If I am 

tall, then I will bump my head”? 

1) If I bump my head, then I am tall. 

2) If I do not bump my head, then I am tall. 

3) If I am tall, then I will not bump my head. 

4) If I do not bump my head, then I am not tall. 

336 In the diagram of circle O below, chord CD is 

parallel to diameter AOB and mAC = 30. 

What is mCD? 

1) 150 

2) 120 

3) 100 

4) 60 

337 What is the equation of a line that is parallel to the 

line whose equation is y = x + 2? 

1) x + y = 5 

2) 2x + y = −2 

3) y − x = −1 

4) y − 2x = 3 

338 The endpoints of AB are A(3,2) and B(7,1). If 

A″B″ is the result of the transformation of AB 

under D 2 T −4,3 what are the coordinates of A″ and 

B″? 

1) A″(−2,10) and B″(6,8) 

2) A″(−1,5) and B″(3,4) 

3) A″(2,7) and B″(10,5) 

4) A″(14,−2) and B″(22,−4) 

339 In the diagram below, tangent AB and secant ACD 

are drawn to circle O from an external point A, 

AB = 8, and AC = 4. 

What is the length of CD? 

1) 16 

2) 13 

3) 12 

4) 10


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340 The diagram below shows AB and DE. 

Which transformation will move AB onto DE such 

that point D is the image of point A and point E is 

the image of point B? 

1) T 3,−3 

2) D 1 

2 

3) R 90° 

4) r y = x 

341 In ABC, AB = 7, BC = 8, and AC = 9. Which 

list has the angles of ABC in order from smallest 

to largest? 

1) ∠A,∠B,∠C 

2) ∠B,∠A,∠C 

3) ∠C,∠B,∠A 

4) ∠C,∠A,∠B 

342 In the diagram below, PS is a tangent to circle O at 

point S, PQR is a secant, PS = x, PQ = 3, and 

PR = x + 18. 

What is the length of PS ? 

1) 6 

2) 9 

3) 3 

4) 27 


whose equation is 2y = −6x + 8? 

1) −3 

1 

2) 

6 

3) 

1 

3 

4) −6 

344 Given: Quadrilateral ABCD with AB ≅ CD, 

AD ≅ BC , and diagonal BD is drawn 

Prove: ∠BDC ≅ ∠ABD


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345 What is the converse of the statement "If Bob does 

his homework, then George gets candy"? 

1) If George gets candy, then Bob does his 

homework. 

2) Bob does his homework if and only if George 

gets candy. 

3) If George does not get candy, then Bob does 

not do his homework. 

4) If Bob does not do his homework, then George 

does not get candy. 

346 In the diagram below of circle C, QR is a diameter, 

and Q(1,8) and C(3.5,2) are points on a coordinate 

plane. Find and state the coordinates of point R. 

347 The lines represented by the equations y + 1 

x = 4 

2 

and 3x + 6y = 12 are 


2) parallel 



348 In the diagram of ABC and DEF below, 

AB ≅ DE, ∠A ≅ ∠D, and ∠B ≅ ∠E. 

Which method can be used to prove 

ABC ≅ DEF? 

1) SSS 

2) SAS 

3) ASA 

4) HL 

349 The diameter of a circle has endpoints at (−2,3) and 

(6,3). What is an equation of the circle? 

1) (x − 2) 2 + (y − 3) 2 = 16 

2) (x − 2) 2 + (y − 3) 2 = 4 

3) (x + 2) 2 + (y + 3) 2 = 16 

4) (x + 2) 2 + (y + 3) 2 = 4 


the point (7,3) and is parallel to the line 

4x + 2y = 10? 

1) y = 1 1 

x − 

2 2 

2) y = − 1 13 

x + 

2 2 

3) y = 2x − 11 

4) y = −2x + 17


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351 Side PQ of PQR is extended through Q to point 

T. Which statement is not always true? 

1) m∠RQT > m∠R 

2) m∠RQT > m∠P 

3) m∠RQT = m∠P + m∠R 

4) m∠RQT > m∠PQR 

352 Juliann plans on drawing ABC, where the 

measure of ∠A can range from 50° to 60° and the 

measure of ∠B can range from 90° to 100°. Given 

these conditions, what is the correct range of 

measures possible for ∠C? 

1) 20° to 40° 

2) 30° to 50° 

3) 80° to 90° 

4) 120° to 130° 

353 In the diagram below, the length of the legs AC and 

BC of right triangle ABC are 6 cm and 8 cm, 

respectively. Altitude CD is drawn to the 

hypotenuse of ABC. 

What is the length of AD to the nearest tenth of a 

centimeter? 

1) 3.6 

2) 6.0 

3) 6.4 

4) 4.0 

354 The equation of a circle is x 2 + (y − 7) 2 = 16. What 

are the center and radius of the circle? 

1) center = (0,7); radius = 4 

2) center = (0,7); radius = 16 

3) center = (0,−7); radius = 4 

4) center = (0,−7); radius = 16 

355 In the diagram below of TEM , medians TB, EC , 

and MA intersect at D, and TB = 9. Find the length 

of TD. 

356 In the diagram below of ABC with side AC 

extended through D, m∠A = 37 and 

m∠BCD = 117. Which side of ABC is the 

longest side? Justify your answer.


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357 In the diagram below, the vertices of DEF are 

the midpoints of the sides of equilateral triangle 

ABC, and the perimeter of ABC is 36 cm. 

What is the length, in centimeters, of EF? 

1) 6 

2) 12 

3) 18 

4) 4 

358 The diagram below shows a pennant in the shape of 

an isosceles triangle. The equal sides each measure 

13, the altitude is x + 7, and the base is 2x. 

What is the length of the base? 

1) 5 

2) 10 

3) 12 

4) 24 

359 A city is planning to build a new park. The park 

must be equidistant from school A at (3,3) and 

school B at (3,−5). The park also must be exactly 5 

miles from the center of town, which is located at 

the origin on the coordinate graph. Each unit on the 

graph represents 1 mile. On the set of axes below, 

sketch the compound loci and label with an X all 

possible locations for the new park. 

360 If the diagonals of a quadrilateral do not bisect 

each other, then the quadrilateral could be a 

1) rectangle 

2) rhombus 

3) square 

4) trapezoid


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361 In the diagram below of ABC, D is a point on 

AB, AC = 7, AD = 6, and BC = 18. 

The length of DB could be 

1) 5 

2) 12 

3) 19 

4) 25 

362 The diagram below illustrates the construction of 

PS → ←⎯ 

parallel to RQ → ←⎯⎯ 

through point P. 

Which statement justifies this construction? 

1) m∠1 = m∠2 

2) m∠1 = m∠3 

3) PR ≅ RQ 

4) PS ≅ RQ 

363 Which graph represents a circle with the equation 

(x − 5) 2 + (y + 1) 2 = 9? 

1) 

2) 

3) 

4)


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364 A circle is represented by the equation 

x 2 + (y + 3) 2 = 13. What are the coordinates of the 

center of the circle and the length of the radius? 

1) (0,3) and 13 

2) (0,3) and 13 

3) (0,−3) and 13 

4) (0,−3) and 13 

365 The vertices of ABC are A(−1,−2), B(−1,2) and 

C(6,0). Which conclusion can be made about the 

angles of ABC? 

1) m∠A = m∠B 

2) m∠A = m∠C 

3) m∠ACB = 90 

4) m∠ABC = 60 

366 Which expression represents the volume, in cubic 

centimeters, of the cylinder represented in the 

diagram below? 

1) 162π 

2) 324π 

3) 972π 

4) 3,888π 

367 What is the length of the line segment with 

endpoints (−6,4) and (2,−5)? 

1) 13 

2) 17 

3) 72 

4) 145 

368 In the diagram below of ABC, AE ≅ BE , 

AF ≅ CF, and CD ≅ BD. 

Point P must be the 

1) centroid 

2) circumcenter 

3) Incenter 

4) orthocenter 

369 In PQR, PQ = 8, QR = 12, and RP = 13. Which 

statement about the angles of PQR must be true? 

1) m∠Q > m∠P > m∠R 

2) m∠Q > m∠R > m∠P 

3) m∠R > m∠P > m∠Q 

4) m∠P > m∠R > m∠Q


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370 Based on the diagram below, which statement is 

true? 

1) a b 

2) a c 

3) b c 

4) d e 

371 In the diagram below of ACD, E is a point on 

AD and B is a point on AC, such that EB DC . If 

AE = 3, ED = 6, and DC = 15, find the length of 

EB. 

372 In three-dimensional space, two planes are parallel 

and a third plane intersects both of the parallel 

planes. The intersection of the planes is a 

1) plane 

2) point 

3) pair of parallel lines 

4) pair of intersecting lines 

373 In the diagram below of right triangle ACB, altitude 

CD intersects AB at D. If AD = 3 and DB = 4, find 

the length of CD in simplest radical form. 

374 In the diagram below of ABC, CD is the bisector 

of ∠BCA, AE is the bisector of ∠CAB, and BG is 

drawn. 


1) DG = EG 

2) AG = BG 

3) ∠AEB ≅ ∠AEC 

4) ∠DBG ≅ ∠EBG


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375 Which transformation produces a figure similar but 

not congruent to the original figure? 

1) T1,3 2) D 1 

2 

3) R90° 4) r y = x 

376 In the diagram of ABC below, AB ≅ AC. The 

measure of ∠B is 40°. 

What is the measure of ∠A? 

1) 40° 

2) 50° 

3) 70° 

4) 100° 

377 The base of a pyramid is a rectangle with a width 

of 6 cm and a length of 8 cm. Find, in centimeters, 

the height of the pyramid if the volume is 288 cm 3 . 

378 What is an equation for the circle shown in the 

graph below? 

1) x 2 + y 2 = 2 

2) x 2 + y 2 = 4 

3) x 2 + y 2 = 8 

4) x 2 + y 2 = 16 

379 Isosceles trapezoid ABCD has diagonals AC and 

BD. If AC = 5x + 13 and BD = 11x − 5, what is the 

value of x? 

1) 28 

2) 10 3 

4 

3) 3 

4) 

1 

2


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380 On the set of axes below, solve the following 

system of equations graphically for all values of x 

and y. 

y = (x − 2) 2 + 4 

4x + 2y = 14 



1) 

3 

4 

2) − 3 

4 

3) 

4 

3 

4) − 4 

3 

382 Point A is not contained in plane B. How many 

lines can be drawn through point A that will be 

perpendicular to plane B? 

1) one 

2) two 

3) zero 

4) infinite 

383 A polygon is transformed according to the rule: 

(x,y) → (x + 2,y). Every point of the polygon 

moves two units in which direction? 

1) up 

2) down 

3) left 

4) right 

384 In the diagram of circle O below, chord AB 

intersects chord CD at E, DE = 2x + 8, EC = 3, 

AE = 4x − 3, and EB = 4. 

What is the value of x? 

1) 1 

2) 3.6 

3) 5 

4) 10.25


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385 A rectangular prism has a volume of 

3x 2 + 18x + 24. Its base has a length of x + 2 and a 

width of 3. Which expression represents the height 

of the prism? 

1) x + 4 

2) x + 2 

3) 3 

4) x 2 + 6x + 8 


bisector of ∠ABC. 


1) m∠EBF = 1 

2 m∠ABC 

2) m∠DBF = 1 

2 m∠ABC 

3) m∠EBF = m∠ABC 

4) m∠DBF = m∠EBF 


bisector of the angle shown below. [Leave all 

construction marks.] 


perpendicular bisector of AB. 


1) AC = CB 

2) CB = 1 

2 AB 

3) AC = 2AB 

4) AC + CB = AB


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389 In the diagram below of isosceles trapezoid DEFG, 

DE GF, DE = 4x − 2, EF = 3x + 2, FG = 5x − 3, 

and GD = 2x + 5. Find the value of x. 

390 Write an equation for circle O shown on the graph 

below. 

391 What is an equation of the line that contains the 

point (3,−1) and is perpendicular to the line whose 

equation is y = −3x + 2? 

1) y = −3x + 8 

2) y = −3x 

3) y = 1 

3 x 

4) y = 1 

x − 2 

3 

392 After a composition of transformations, the 

coordinates A(4,2), B(4,6), and C(2,6) become 

A″(−2,−1), B″(−2,−3), and C ″(−1,−3), as shown on 

the set of axes below. 

Which composition of transformations was used? 

1) R180° D 2 

2) R90° D 2 

3) D 1 

2 

R180° 4) D 1 

2 

R90°


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393 The diagram below shows the construction of a line 

through point P perpendicular to line m. 

Which statement is demonstrated by this 

construction? 

1) If a line is parallel to a line that is 

perpendicular to a third line, then the line is 

also perpendicular to the third line. 

2) The set of points equidistant from the 

endpoints of a line segment is the 

perpendicular bisector of the segment. 

3) Two lines are perpendicular if they are 

equidistant from a given point. 

4) Two lines are perpendicular if they intersect to 

form a vertical line. 

394 Tangents PA and PB are drawn to circle O from an 

external point, P, and radii OA and OB are drawn. 

If m∠APB = 40, what is the measure of ∠AOB? 

1) 140º 

2) 100º 

3) 70º 

4) 50º 

395 A transformation of a polygon that always 

preserves both length and orientation is 





396 What is the length, to the nearest tenth, of the line 

segment joining the points (−4,2) and (146,52)? 

1) 141.4 

2) 150.5 

3) 151.9 

4) 158.1 

397 Which equation represents circle K shown in the 

graph below? 

1) (x + 5) 2 + (y − 1) 2 = 3 

2) (x + 5) 2 + (y − 1) 2 = 9 

3) (x − 5) 2 + (y + 1) 2 = 3 

4) (x − 5) 2 + (y + 1) 2 = 9


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398 Two lines are represented by the equations 

− 1 

y = 6x + 10 and y = mx. For which value of m 

2 

will the lines be parallel? 

1) −12 

2) −3 

3) 3 

4) 12 

399 In the diagram below, ABC is inscribed in circle 

P. The distances from the center of circle P to each 

side of the triangle are shown. 

Which statement about the sides of the triangle is 

true? 

1) AB > AC > BC 

2) AB < AC and AC > BC 

3) AC > AB > BC 

4) AC = AB and AB > BC 

400 In isosceles trapezoid ABCD, AB ≅ CD. If 

BC = 20, AD = 36, and AB = 17, what is the length 

of the altitude of the trapezoid? 

1) 10 

2) 12 

3) 15 

4) 16 

401 Find an equation of the line passing through the 

point (6,5) and perpendicular to the line whose 

equation is 2y + 3x = 6. 

402 In the diagram below, circle A and circle B are 

shown. 

What is the total number of lines of tangency that 

are common to circle A and circle B? 

1) 1 

2) 2 

3) 3 

4) 4 

403 Given ABC ∼ DEF such that AB 3 

= . Which 

DE 2 

statement is not true? 

1) 

BC 3 

= 

EF 2 

2) m∠A 3 

= 

m∠D 2 

3) 

area of 

area of 

ABC 9 

= 

DEF 4 

4) 

perimeter of 

perimeter of 

ABC 3 

= 

DEF 2


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404 In the diagram below, ABC ∼ EFG, 

m∠C = 4x + 30, and m∠G = 5x + 10. Determine 

the value of x. 

405 If the endpoints of AB are A(−4,5) and B(2,−5), 

what is the length of AB? 

1) 2 34 

2) 2 

3) 61 

4) 8 

406 The diagonal AC is drawn in parallelogram ABCD. 

Which method can not be used to prove that 

ABC ≅ CDA? 

1) SSS 

2) SAS 

3) SSA 

4) ASA 

407 In ABC, point D is on AB, and point E is on BC 

such that DE AC. If DB = 2, DA = 7, and 

DE = 3, what is the length of AC? 

1) 8 

2) 9 

3) 10.5 

4) 13.5 

408 Which transformation of the line x = 3 results in an 

image that is perpendicular to the given line? 

1) r x-axis 

2) r y-axis 

3) r y = x 

4) r x = 1 

409 Given: y = 1 

x − 3 

4 

y = x 2 + 8x + 12 

In which quadrant will the graphs of the given 

equations intersect? 

1) I 

2) II 

3) III 

4) IV 

410 In plane P, lines m and n intersect at point A. If 

line k is perpendicular to line m and line n at point 

A, then line k is 

1) contained in plane P 

2) parallel to plane P 

3) perpendicular to plane P 

4) skew to plane P


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411 Two lines, AB → ←⎯ 

and CRD → ←⎯⎯⎯ 

, are parallel and 10 

inches apart. Sketch the locus of all points that are 

equidistant from AB → ←⎯ 

and CRD → ←⎯⎯⎯ 

and 7 inches from 

point R. Label with an X each point that satisfies 

both conditions. 

412 In which triangle do the three altitudes intersect 

outside the triangle? 

1) a right triangle 

2) an acute triangle 

3) an obtuse triangle 

4) an equilateral triangle 

413 One step in a construction uses the endpoints of AB 

to create arcs with the same radii. The arcs 

intersect above and below the segment. What is 

the relationship of AB and the line connecting the 

points of intersection of these arcs? 

1) collinear 

2) congruent 

3) parallel 


414 Given the equations: y = x 2 − 6x + 10 

y + x = 4 

What is the solution to the given system of 

equations? 

1) (2,3) 

2) (3,2) 

3) (2,2) and (1,3) 

4) (2,2) and (3,1) 

415 Square LMNO is shown in the diagram below. 

What are the coordinates of the midpoint of 

diagonal LN ? 

1) 4 1 

1 

,−2 

2 2 

2) −3 1 

1 

,3 

2 2 

3) −2 1 

1 

,3 

2 2 

4) −2 1 

1 

,4 

2 2


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416 In the diagram below of PRT, Q is a point on 

PR, S is a point on TR, QS is drawn, and 

∠RPT ≅ ∠RSQ. 

Which reason justifies the conclusion that 

PRT ∼ SRQ? 

1) AA 

2) ASA 

3) SAS 

4) SSS 

417 On the line segment below, use a compass and 

straightedge to construct equilateral triangle ABC. 


418 Which geometric principle is used in the 

construction shown below? 

1) The intersection of the angle bisectors of a 

triangle is the center of the inscribed circle. 

2) The intersection of the angle bisectors of a 

triangle is the center of the circumscribed 

circle. 

3) The intersection of the perpendicular bisectors 

of the sides of a triangle is the center of the 

inscribed circle. 

4) The intersection of the perpendicular bisectors 

of the sides of a triangle is the center of the 

circumscribed circle. 

419 Which set of numbers represents the lengths of the 

sides of a triangle? 

1) {5,18,13} 

2) {6,17,22} 

3) {16,24,7} 

4) {26,8,15}


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420 Write an equation of the circle whose diameter AB 

has endpoints A(−4,2) and B(4,−4). [The use of 

the grid below is optional.] 

421 In the diagram of ABC below, AB = 10, BC = 14, 

and AC = 16. Find the perimeter of the triangle 

formed by connecting the midpoints of the sides of 

ABC. 


whose equation is 5x + 3y = 8? 

1) 

5 

3 

2) 

3 

5 

3) − 3 

5 

4) − 5 

3 


angle bisector of ∠ABC shown below. [Leave all 



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424 In the diagram below, a right circular cone has a 

diameter of 8 inches and a height of 12 inches. 

What is the volume of the cone to the nearest cubic 

inch? 

1) 201 

2) 481 

3) 603 

4) 804 

425 In which polygon does the sum of the measures of 

the interior angles equal the sum of the measures of 

the exterior angles? 

1) triangle 

2) hexagon 

3) octagon 

4) quadrilateral 


whose equation is y = 3x + 4? 

1) 

1 

3 

2) − 1 

3 

3) 3 

4) −3 

427 Which equation represents a line perpendicular to 


1) 6y = −4x + 12 

2) 2y = 3x + 6 

3) 2y = −3x + 6 

4) 3y = −2x + 12 

428 ABC is similar to DEF. The ratio of the 

length of AB to the length of DE is 3:1. Which 

ratio is also equal to 3:1? 

1) m∠A 

m∠D 

2) m∠B 

m∠F 

3) 

area of ABC 

4) 

area of DEF 

perimeter of ABC 

perimeter of DEF 

429 The figure in the diagram below is a triangular 

prism. 


1) DE ≅ AB 

2) AD ≅ BC 

3) AD CE 

4) DE BC


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430 In ABC, m∠A = 95, m∠B = 50, and m∠C = 35. 

Which expression correctly relates the lengths of 

the sides of this triangle? 

1) AB < BC < CA 

2) AB < AC < BC 

3) AC < BC < AB 

4) BC < AC < AB 

431 Triangle DEG has the coordinates D(1,1), E(5,1), 

and G(5,4). Triangle DEG is rotated 90° about the 

origin to form D′E ′G′. On the grid below, graph 

and label DEG and D′E ′G′. State the 

coordinates of the vertices D', E', and G'. Justify 

that this transformation preserves distance. 

432 Which diagram shows the construction of an 

equilateral triangle? 

1) 

2) 

3) 

4)


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433 In the diagram below of trapezoid RSUT, RS TU , 

X is the midpoint of RT , and V is the midpoint of 

SU . 

If RS = 30 and XV = 44, what is the length of TU ? 

1) 37 

2) 58 

3) 74 

4) 118 

434 In the diagram of trapezoid ABCD below, diagonals 

AC and BD intersect at E and ABC ≅ DCB. 

Which statement is true based on the given 

information? 

1) AC ≅ BC 

2) CD ≅ AD 

3) ∠CDE ≅ ∠BAD 

4) ∠CDB ≅ ∠BAC 

435 Point A is located at (4,−7). The point is reflected 

in the x-axis. Its image is located at 

1) (−4,7) 

2) (−4,−7) 

3) (4,7) 

4) (7,−4) 

436 In the diagram below, ABC is shown with AC 

extended through point D. 

If m∠BCD = 6x + 2, m∠BAC = 3x + 15, and 

m∠ABC = 2x − 1, what is the value of x? 

1) 12 

2) 14 10 

11 

3) 16 

4) 18 1 

9 

437 The degree measures of the angles of ABC are 

represented by x, 3x, and 5x − 54. Find the value of 

x.


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438 In the diagram of ABC below, Jose found 

centroid P by constructing the three medians. He 

measured CF and found it to be 6 inches. 

If PF = x, which equation can be used to find x? 

1) x + x = 6 

2) 2x + x = 6 

3) 3x + 2x = 6 

4) x + 2 

x = 6 

3 

439 Towns A and B are 16 miles apart. How many 

points are 10 miles from town A and 12 miles from 

town B? 

1) 1 

2) 2 

3) 3 

4) 0 

440 The volume of a cylinder is 12,566.4 cm 3 . The 

height of the cylinder is 8 cm. Find the radius of 

the cylinder to the nearest tenth of a centimeter. 

441 A support beam between the floor and ceiling of a 

house forms a 90º angle with the floor. The builder 

wants to make sure that the floor and ceiling are 

parallel. Which angle should the support beam 

form with the ceiling? 

1) 45º 

2) 60º 

3) 90º 

4) 180º 

442 Which equation represents a line parallel to the line 

whose equation is 2y − 5x = 10? 

1) 5y − 2x = 25 

2) 5y + 2x = 10 

3) 4y − 10x = 12 

4) 2y + 10x = 8 

443 Point P is on line m. What is the total number of 

planes that are perpendicular to line m and pass 

through point P? 

1) 1 

2) 2 

3) 0 

4) infinite


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444 Using a compass and straightedge, on the diagram 

below of RS → ←⎯ 

, construct an equilateral triangle with 

RS as one side. [Leave all construction marks.] 

445 In the diagram below of circle O, chords DF, DE, 

FG, and EG are drawn such that 

mDF :mFE :mEG :mGD = 5:2:1:7. Identify one 

pair of inscribed angles that are congruent to each 

other and give their measure. 

446 In the diagram below, SQ and PR intersect at T, 

PQ is drawn, and PS QR. 

What technique can be used to prove that 

PST ∼ RQT? 

1) SAS 

2) SSS 

3) ASA 

4) AA 

447 Which equation represents the circle whose center 

is (−2,3) and whose radius is 5? 

1) (x − 2) 2 + (y + 3) 2 = 5 

2) (x + 2) 2 + (y − 3) 2 = 5 

3) (x + 2) 2 + (y − 3) 2 = 25 

4) (x − 2) 2 + (y + 3) 2 = 25


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448 In the diagram below of parallelogram ABCD with 

diagonals AC and BD, m∠1 = 45 and 

m∠DCB = 120. 

What is the measure of ∠2? 

1) 15º 

2) 30º 

3) 45º 

4) 60º 


C(4,0). Under a translation, A′, the image point of 

A, is located at (4,4). Under this same translation, 

point C ′ is located at 

1) (7,1) 

2) (5,3) 

3) (3,2) 

4) (1,−1) 

450 Given: JKLM is a parallelogram. 

JM ≅ LN 

∠LMN ≅ ∠LNM 

Prove: JKLM is a rhombus. 

451 What is the negation of the statement “The Sun is 

shining”? 

1) It is cloudy. 

2) It is daytime. 

3) It is not raining. 

4) The Sun is not shining. 

452 In the diagram below, under which transformation 

will A′B′C ′ be the image of ABC? 





453 Line segment AB is tangent to circle O at A. Which 

type of triangle is always formed when points A, B, 

and O are connected? 

1) right 

2) obtuse 

3) scalene 

4) isosceles


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454 Which illustration shows the correct construction 

of an angle bisector? 

1) 

2) 

3) 

4) 

455 Which graph could be used to find the solution to 

the following system of equations? 

y = −x + 2 

1) 

2) 

3) 

4) 

y = x 2


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456 The length of AB is 3 inches. On the diagram below, sketch the points that are equidistant from A and B and 

sketch the points that are 2 inches from A. Label with an X all points that satisfy both conditions.


Answer Section 

1 ANS: 

PTS: 4 REF: 061137ge STA: G.G.70 TOP: Quadratic-Linear Systems 

2 ANS: 4 

d = (−5 − 3) 2 + (4 − (−6)) 2 = 64 + 100 = 164 = 4 41 = 2 41 

PTS: 2 

KEY: general 

REF: 011121ge STA: G.G.67 TOP: Distance 

3 ANS: 1 

TOP: Negations 

4 ANS: 1 

PTS: 2 REF: 011213ge STA: G.G.24 

3x + 5 + 4x − 15 + 2x + 10 = 180. 

m∠D = 3(20) + 5 = 65. m∠E = 4(20) − 15 = 65. 

9x = 180 

x = 20 

ID: A 

PTS: 2 REF: 061119ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles 

5 ANS: 

Quadrilateral ABCD, AD ≅ BC and ∠DAE ≅ ∠BCE are given. AD BC because if two lines are cut by a 

transversal so that a pair of alternate interior angles are congruent, the lines are parallel. ABCD is a parallelogram 

because if one pair of opposite sides of a quadrilateral are both congruent and parallel, the quadrilateral is a 

parallelogram. AE ≅ CE because the diagonals of a parallelogram bisect each other. ∠FEA ≅ ∠GEC as vertical 

angles. AEF ≅ CEG by ASA. 

PTS: 6 REF: 011238ge STA: G.G.27 TOP: Quadrilateral Proofs 

6 ANS: 2 PTS: 2 REF: 011215ge STA: G.G.12 

TOP: Volume

7 ANS: 

30. 

PTS: 2 REF: 011129ge STA: G.G.31 TOP: Isosceles Triangle Theorem 


TOP: Identifying Transformations 

9 ANS: 3 

TOP: Solids 



TOP: Constructions 


TOP: Graphing Circles 

12 ANS: 

16.7. x 12 

= 

25 18 

18x = 300 

x ≈ 16.7 

PTS: 2 REF: 061133ge STA: G.G.46 TOP: Side Splitter Theorem 

13 ANS: 

PTS: 2 REF: 081233ge STA: G.G.19 TOP: Constructions 

14 ANS: 2 

The slope of a line in standard form is −A 

B 

ID: A 

−4 

, so the slope of this line is . A parallel line would also have a slope 

3 

of −4 

. Since the answers are in standard form, use the point-slope formula. y − 2 = −4 (x + 5) 

3 3 

3y − 6 = −4x − 20 

4x + 3y = −14 

PTS: 2 

15 ANS: 

REF: 061123ge STA: G.G.65 TOP: Parallel and Perpendicular Lines 

L = 2πrh = 2π ⋅ 12 ⋅ 22 ≈ 1659. 1659 

≈ 2.8. 3 cans are needed. 

600 

PTS: 2 REF: 061233ge STA: G.G.14 TOP: Lateral Area

16 ANS: 1 

 

8 + 0 

m = 

2 

, 2 + 6 

2 

 

 

6 − 2 4 

= (4,4) m = = = −1 

0 − 8 −8 2 m⊥ = 2 y = mx + b 

4 = 2(4) + b 

−4 = b 

PTS: 2 

17 ANS: 4 

m⊥ = − 

REF: 081126ge STA: G.G.68 TOP: Perpendicular Bisector 

1 

. y = mx + b 

3 

6 = − 1 

(−9) + b 

3 

6 = 3 + b 

3 = b 

PTS: 2 REF: 061215ge STA: G.G.64 TOP: Parallel and Perpendicular Lines 

18 ANS: 

PTS: 2 REF: 011130ge STA: G.G.54 TOP: Reflections 

KEY: grids 

19 ANS: 2 

7x = 5x + 30 

2x = 30 

x = 15 

PTS: 2 

20 ANS: 

REF: 061106ge STA: G.G.35 TOP: Parallel Lines and Transversals 

(5 − 2)180 = 540. 540 

= 108 interior. 180 − 108 = 72 exterior 

5 

ID: A 

PTS: 2 REF: 011131ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons 


TOP: Triangle Congruency 


TOP: Quadrilateral Proofs

23 ANS: 

32. 

16 x − 3 

= 

20 x + 5 

16x + 80 = 20x − 60 

140 = 4x 

35 = x 

. AC = x − 3 = 35 − 3 = 32 


24 ANS: 


25 ANS: 

A′(5,−4), B′(5,1), C ′(2,1), D′(2,−6); A″(5,4), B″(5,−1), C ″(2,−1), D″(2,6) 

PTS: 4 

KEY: grids 

REF: 061236ge STA: G.G.58 TOP: Compositions of Transformations 

26 ANS: 3 

 

180(n − 2) 

180(n − 2) = n 180 − 

n 

 

 

180n − 360 = 180n − 180n + 360 

180n = 720 

n = 4 

ID: A 

PTS: 2 REF: 081223ge STA: G.G.36 TOP: Interior and Exterior Angles of Polygons

27 ANS: 

2 

x + 2 

x 

= x + 6 

4 

x 2 + 6x = 4x + 8 

x 2 + 2x − 8 = 0 

(x + 4)(x − 2) = 0 

x = 2 

PTS: 4 REF: 081137ge STA: G.G.45 TOP: Similarity 

KEY: basic 

28 ANS: 4 

−3 + x 

−5 = . 2 = 

2 

−10 = −3 + x 

−7 = x 

6 + y 

2 

4 = 6 + y 

−2 = y 

ID: A 

PTS: 2 REF: 081203ge STA: G.G.66 TOP: Midpoint 


TOP: Parallelograms 



31 ANS: 

∠B and ∠E are right angles because of the definition of perpendicular lines. ∠B ≅ ∠E because all right angles 

are congruent. ∠BFD and ∠DFE are supplementary and ∠ECA and ∠ACB are supplementary because of the 

definition of supplementary angles. ∠DFE ≅ ∠ACB because angles supplementary to congruent angles are 

congruent. ABC ∼ DEF because of AA. 

PTS: 4 REF: 011136ge STA: G.G.44 TOP: Similarity Proofs 

32 ANS: 

PTS: 2 REF: 011230ge STA: G.G.22 TOP: Locus 


TOP: Centroid, Orthocenter, Incenter and Circumcenter 

34 ANS: 2 

4x + 10 

= 2x + 5 

2 

PTS: 2 REF: 011103ge STA: G.G.42 TOP: Midsegments


TOP: Parallelograms 

36 ANS: 4 

y = mx + b 

3 = 3 

(−2) + b 

2 

3 = −3 + b 

6 = b 



TOP: Planes 



39 ANS: 3 

PTS: 2 REF: 011112ge STA: G.G.49 TOP: Chords 

40 ANS: 1 

40 − 24 

2 

= 8. 10 2 − 8 2 = 6. 

PTS: 2 

41 ANS: 1 

REF: 061204ge STA: G.G.40 TOP: Trapezoids 

−4 + x 

1 = . 

2 

3 + y 

5 = . 

2 

−4 + x = 2 

x = 6 

3 + y = 10 

y = 7 


ID: A

42 ANS: 

PTS: 2 

43 ANS: 3 

REF: 061232ge STA: G.G.17 TOP: Constructions 

x + 2x + 15 = 5x + 15 2(5) + 15 = 25 

3x + 15 = 5x + 5 

10 = 2x 

5 = x 

PTS: 2 REF: 011127ge STA: G.G.32 TOP: Exterior Angle Theorem 

44 ANS: 


45 ANS: 2 

The slope of x + 2y = 3 is m = −A 

B 

= −1 

2 . m ⊥ 

= 2. 

PTS: 2 

46 ANS: 2 


(n − 2)180 = (6 − 2)180 = 720. 720 

= 120. 

6 

ID: A 

PTS: 2 

47 ANS: 3 

3 

× 180 = 36 

8 + 3 + 4 

REF: 081125ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons 

PTS: 2 REF: 011210ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles

48 ANS: 

52, 40, 80. 360 − (56 + 112) = 192. 

192 − 112 

1 

× 192 = 48 

4 

56 + 48 

2 

= 52 

2 

= 40. 

112 + 48 

2 

PTS: 6 REF: 081238ge STA: G.G.51 TOP: Arcs Determined by Angles 

KEY: inscribed 

49 ANS: 

V = πr 2 h 

600π = πr 2 ⋅ 12 

50 = r 2 

25 2 = r 

5 2 = r 

. L = 2πrh = 2π ⋅ 5 2 ⋅ 12 ≈ 533.1 

= 80 

PTS: 4 REF: 011236ge STA: G.G.14 TOP: Volume 

50 ANS: 

No, ∠KGH is not congruent to ∠GKH . 



TOP: Properties of Transformations 


TOP: Similarity Proofs 


TOP: Reflections KEY: basic 

54 ANS: 

2 is not a prime number, false. 

PTS: 2 REF: 081229ge STA: G.G.24 TOP: Negations 


TOP: Special Parallelograms 

ID: A

56 ANS: 



TOP: Locus 

58 ANS: 4 

PTS: 2 REF: 081114ge STA: G.G.28 TOP: Triangle Congruency 

59 ANS: 4 

Parallel lines intercept congruent arcs. 

PTS: 2 

60 ANS: 

REF: 081201ge STA: G.G.52 TOP: Chords 

(−4 − 2) 2 + (3 − 5) 2 = 36 + 4 = 40 = 4 10 = 2 10 . 

PTS: 2 REF: 081232ge STA: G.G.67 TOP: Distance 


TOP: Exterior Angle Theorem 



63 ANS: 2 

7 + (−3) 

M x = = 2. M Y = 

2 

−1 + 3 

2 

= 1. 



TOP: Planes 

ID: A


TOP: Equations of Circles 




TOP: Planes 


TOP: Interior and Exterior Angles of Polygons 



70 ANS: 

180 − (90 + 63) = 27 

ID: A 

PTS: 2 REF: 061230ge STA: G.G.35 TOP: Parallel Lines and Transversals 

71 ANS: 4 

AB is a vertical line, so its perpendicular bisector is a horizontal line through the midpoint of AB, which is (0,3). 

PTS: 2 REF: 011225ge STA: G.G.68 TOP: Perpendicular Bisector 

72 ANS: 4 

6 2 = x(x + 5) 

36 = x 2 + 5x 

0 = x 2 + 5x − 36 

0 = (x + 9)(x − 4) 

x = 4 


KEY: leg 




TOP: Compound Statements KEY: conjunction 

75 ANS: 3 

(3,−2) → (2,3) → (8,12) 

PTS: 2 REF: 011126ge STA: G.G.54 TOP: Compositions of Transformations 

KEY: basic 

76 ANS: 3 

−5 + 3 = −2 2 + −4 = −2 

PTS: 2 REF: 011107ge STA: G.G.54 TOP: Translations

77 ANS: 

 

(7,5) m AB = 

 

3 + 7 

2 

3 + 9 

, 

2 

= (5,6) m 7 + 11 

BC = , 

2 

9 + 3 

 

 

2 



78 ANS: 

V = 4 

3 π ⋅ 93 = 972π 

 

= (9,6) 

 

PTS: 2 REF: 081131ge STA: G.G.16 TOP: Surface Area 

79 ANS: 

9.1. (11)(8)h = 800 

h ≈ 9.1 

PTS: 2 

80 ANS: 3 

180 − 70 

= 55 

2 

REF: 061131ge STA: G.G.12 TOP: Volume 


81 ANS: 4 

6 2 − 2 2 = 32 = 16 2 = 4 2 




83 ANS: 4 

m∠A = 80 

PTS: 2 REF: 011115ge STA: G.G.34 TOP: Angle Side Relationship 

84 ANS: 3 

y = mx + b 

−1 = 2(2) + b 

−5 = b 




ID: A






TOP: Planes 


TOP: Similarity KEY: basic 

90 ANS: 

Yes. A reflection is an isometry. 

PTS: 2 REF: 061132ge STA: G.G.56 TOP: Identifying Transformations 



92 ANS: 2 

m = −A 

B 

= −4 

2 

= −2 y = mx + b 

2 = −2(2) + b 

6 = b 


93 ANS: 1 


94 ANS: 

PTS: 2 

95 ANS: 

180 − 80 

= 50 

2 



ID: A

96 ANS: 2 

AC = BD 

AC − BC = BD − BC 

AB = CD 

PTS: 2 REF: 061206ge STA: G.G.27 TOP: Line Proofs 




TOP: Arcs Determined by Angles KEY: inscribed 

99 ANS: 1 

m = 3 

2 

y = mx + b 

2 = 3 

(1) + b 

2 

1 

= b 

2 

ID: A 





TOP: Planes 


TOP: Parallel and Perpendicular Lines 


TOP: Planes 

104 ANS: 

OA ≅ OB because all radii are equal. OP ≅ OP because of the reflexive property. OA⊥ PA and OB⊥ PB 

because tangents to a circle are perpendicular to a radius at a point on a circle. ∠PAO and ∠PBO are right angles 

because of the definition of perpendicular. ∠PAO ≅ ∠PBO because all right angles are congruent. 

AOP ≅ BOP because of HL. ∠AOP ≅ ∠BOP because of CPCTC. 

PTS: 6 REF: 061138ge STA: G.G.27 TOP: Circle Proofs

105 ANS: 

A' (−2,1), B' (−3,−4), and C' (5,−3) 

PTS: 2 REF: 081230ge STA: G.G.54 TOP: Rotations 



107 ANS: 3 

d = (−1 − 4) 2 + (0 − (−3)) 2 = 25 + 9 = 34 


KEY: general 

108 ANS: 


109 ANS: 2 

m = −A 

B 

= −20 

−2 = 10. m ⊥ 

= − 1 

10 





TOP: Planes 

112 ANS: 3 

The slope of 9x − 3y = 27 is m = −A 

B 

−9 

= = 3, which is the opposite reciprocal of −1 

−3 3 . 


ID: A

113 ANS: 4 

The slope of 3x + 5y = 4 is m = −A 

B 

= −3 

5 . m ⊥ 

= 5 

3 . 


114 ANS: 

R′(−3,−2), S' (−4,4), and T ′(2,2). 

PTS: 2 REF: 011232ge STA: G.G.54 TOP: Rotations 

115 ANS: 

3a + a − 6 

(2a − 3,3b + 2). , 

2 

2b − 1 + 4b + 5 

 

 

4a − 6 

= , 

 

2 2 

6b + 4 

 

 

= (2a − 3,3b + 2) 

2 


116 ANS: 

The slope of y = 2x + 3 is 2. The slope of 2y + x = 6 is −A 

B 

lines are perpendicular. 

ID: A 

−1 

= . Since the slopes are opposite reciprocals, the 

2 



TOP: Planes 

118 ANS: 4 

x 2 − 6x + 2x − 3 = 9x + 27 

x 2 − 4x − 3 = 9x + 27 

x 2 − 13x − 30 = 0 

(x − 15)(x + 2) = 0 

x = 15, − 2 


119 ANS: 

 

M 

 

−7 + 5 

2 

, 2 + 4 

2 

 

 

3 + 5 

= M(−1,3). N 

 

2 

, −4 + 4 

2 

 

= N(4,0). MN is a midsegment. 

 

PTS: 4 REF: 011237ge STA: G.G.42 TOP: Midsegments 


TOP: Special Parallelograms


TOP: Centroid 



123 ANS: 

(x − 5) 2 + (y + 4) 2 = 36 

PTS: 2 REF: 081132ge STA: G.G.72 TOP: Equations of Circles 

124 ANS: 3 

8 2 + 24 2 ≠ 25 2 

PTS: 2 REF: 011111ge STA: G.G.48 TOP: Pythagorean Theorem 





127 ANS: 3 


128 ANS: 

G″(3,3),H ″(7,7),S ″(−1,9) 




130 ANS: 1 

 

The diagonals of a parallelogram intersect at their midpoints. M AC 

 

 

1 + 3 

2 

, 5 + (−1) 

2 

 

= (2,2) 

 

ID: A 

PTS: 2 REF: 061209ge STA: G.G.69 TOP: Quadrilaterals in the Coordinate Plane

131 ANS: 1 

d = (4 − 1) 2 + (7 − 11) 2 = 9 + 16 = 25 = 5 


KEY: general 



133 ANS: 2 

The diagonals of a rhombus are perpendicular. 180 − (90 + 12) = 78 

PTS: 2 REF: 011204ge STA: G.G.39 TOP: Special Parallelograms 

134 ANS: 2 

5 − 3 = 2,5 + 3 = 8 

PTS: 2 REF: 011228ge STA: G.G.33 TOP: Triangle Inequality Theorem 

135 ANS: 3 

4x + 14 + 8x + 10 = 180 

12x = 156 

x = 13 



TOP: Similarity KEY: basic 



138 ANS: 

A′(7,−4),B′(7,−1). C ′(9,−4). The areas are equal because translations preserve distance. 

PTS: 4 REF: 011235ge STA: G.G.55 TOP: Properties of Transformations 


TOP: Tangents KEY: point of tangency 




TOP: Volume 


TOP: Compound Statements KEY: general 

ID: A

143 ANS: 

EO = 6. CE = 10 2 − 6 2 = 8 




145 ANS: 2 

TOP: Locus 

146 ANS: 2 


V = 4 

3 π r 3 = 4 

3 

 

15 

π ⋅ 

2 

3 

≈ 1767.1 

PTS: 2 REF: 061207ge STA: G.G.16 TOP: Volume and Surface Area 

147 ANS: 4 

The centroid divides each median into segments whose lengths are in the ratio 2 : 1. 

PTS: 2 REF: 081220ge STA: G.G.43 TOP: Centroid 

148 ANS: 3 

7x 

4 

= 7 

x 

7x 2 = 28 

x = 2 

. 7(2) = 14 


KEY: basic 


TOP: Angle Proofs 

150 ANS: 

m = −A 

B 

= 6 

2 = 3. m ⊥ 

= −1 

3 . 


151 ANS: 2 

V = πr 2 h = π ⋅ 6 2 ⋅ 15 = 540π 

PTS: 2 

152 ANS: 3 


x 2 + 7 2 = (x + 1) 2 

x + 1 = 25 

x 2 + 49 = x 2 + 2x + 1 

48 = 2x 

24 = x 


ID: A



154 ANS: 4 

TOP: Planes 

155 ANS: 2 


V = 4 

3 π r 3 = 4 

3 π ⋅ 33 = 36π 


156 ANS: 1 

AB = CD 

AB + BC = CD + BC 

AC = BD 

PTS: 2 REF: 081207ge STA: G.G.27 TOP: Line Proofs 

157 ANS: 

T ′(−6,3), A′(−3,3),P ′(−3,−1) 

PTS: 2 REF: 061229ge STA: G.G.54 TOP: Translations 

158 ANS: 3 

bisect each other. 

ID: A 

. Opposite sides of a parallelogram are congruent and the diagonals of a parallelogram 


159 ANS: 

∠ACB ≅ ∠AED is given. ∠A ≅ ∠A because of the reflexive property. Therefore ABC ∼ ADE because of 

AA. 

PTS: 2 REF: 081133ge STA: G.G.44 TOP: Similarity Proofs 


TOP: Special Parallelograms

161 ANS: 3 

8 

2 

= 12 

x 

8x = 24 

x = 3 

. 


162 ANS: 1 




TOP: Midsegments 

164 ANS: 

11. x 2 + 6x = x + 14. 

6(2) − 1 = 11 

x 2 + 5x − 14 = 0 

(x + 7)(x − 2) = 0 

x = 2 

PTS: 2 

165 ANS: 4 

REF: 081235ge STA: G.G.38 TOP: Parallelograms 

25 2 2 

26 − 12 

− 

 

2 

 

= 24 

ID: A 

PTS: 2 REF: 011219ge STA: G.G.40 TOP: Trapezoids 

166 ANS: 2 

TOP: Planes 


167 ANS: 

−6 + 2 

m AB = , 

2 

−2 + 8 

 

 

2 

= D(2,3) m 

2 + 6 8 + −2 

BC = , = E(4,3) F(0,−2). To prove that ADEF is a 

2 2 

parallelogram, show that both pairs of opposite sides of the parallelogram are parallel by showing the opposite 

3 − −2 5 

sides have the same slope: m AD = = AF DE because all horizontal lines have the same slope. ADEF 

−2 − −6 4 

3 − −2 5 

mFE = = 

4 − 0 4 

is not a rhombus because not all sides are congruent. AD = 5 2 + 4 2 = 41 AF = 6 

PTS: 6 REF: 081138ge STA: G.G.69 TOP: Quadrilaterals in the Coordinate Plane



169 ANS: 4 

5 

× 180 = 90 

2 + 3 + 5 

ID: A 








173 ANS: 2 

17 2 − 15 2 = 8. 17 − 8 = 9 

PTS: 2 

174 ANS: 4 


x ⋅ 4x = 6 2 

. PQ = 4x + x = 5x = 5(3) = 15 

4x 2 = 36 

x = 3 


KEY: leg 

175 ANS: 

30. 3x + 4x + 5x = 360. 

mLN : mNK :mKL = 90:120:150. 

x = 20 

150 − 90 

2 


KEY: outside circle 

176 ANS: 2 

d = (−1 − 7) 2 + (9 − 4) 2 = 64 + 25 = 89 

= 30 


KEY: general 


TOP: Triangles in the Coordinate Plane 


TOP: Solids

179 ANS: 

2x − 20 = x + 20. 

mAB = x + 20 = 40 + 20 = 60 

x = 40 

PTS: 2 

180 ANS: 1 


7x + 4 = 2(2x + 5) . PM = 2(2) + 5 = 9 

7x + 4 = 4x + 10 

3x = 6 

x = 2 


181 ANS: 1 

The length of the midsegment of a trapezoid is the average of the lengths of its bases. 

x + 3 + 5x − 9 

2 

ID: A 

= 2x + 2. 

6x − 6 = 4x + 4 

2x = 10 


182 ANS: 

∠B and ∠C are right angles because perpendicular lines form right angles. ∠B ≅ ∠C because all right 

angles are congruent. ∠AEB ≅ ∠DEC because vertical angles are congruent. ABE ≅ DCE because of 

ASA. AB ≅ DC because CPCTC. 

PTS: 4 REF: 061235ge STA: G.G.27 TOP: Triangle Proofs 

183 ANS: 4 

20 + 8 + 10 + 6 = 44. 


x = 5

184 ANS: 


185 ANS: 1 


186 ANS: 2 

3x + x + 20 + x + 20 = 180 

5x = 40 

x = 28 



TOP: Planes 

188 ANS: 3 

d = (1 − 9) 2 + (−4 − 2) 2 = 64 + 36 = 100 = 10 


KEY: general 

189 ANS: 

The medians of a triangle are not concurrent. False. 

PTS: 2 REF: 061129ge STA: G.G.24 TOP: Negations 



191 ANS: 3 

The slope of 2y = x + 2 is 1 

, which is the opposite reciprocal of −2. 3 = −2(4) + b 

2 

11 = b 


ID: A

192 ANS: 

The slope of x + 2y = 4 is m = −A −1 

−A 2 

= . The slope of 4y − 2x = 12 is = 

B 2 B 4 

equal nor opposite reciprocals, the lines are neither parallel nor perpendicular. 

ID: A 

1 

= . Since the slopes are neither 

2 


193 ANS: 4 

m = −A 

B 

−3 

= . y = mx + b 

2 

−1 = −3 

 

(2) + b 

2 

−1 = −3 + b 

2 = b 

PTS: 2 

194 ANS: 4 


25 2 − 7 2 = 24 

PTS: 2 REF: 081105ge STA: G.G.50 TOP: Tangents 

KEY: point of tangency 

195 ANS: 3 

5 2 + 12 2 = 13 

PTS: 2 

196 ANS: 2 

50 + x 

= 34 

2 

50 + x = 68 

x = 18 

REF: 061116ge STA: G.G.39 TOP: Special Parallelograms 

PTS: 2 

KEY: inside circle 

REF: 011214ge STA: G.G.51 TOP: Arcs Determined by Angles 




TOP: Angle Side Relationship 

199 ANS: 2 

6x + 42 = 18x − 12 

54 = 12x 

x = 54 

= 4.5 

12 

PTS: 2 REF: 011201ge STA: G.G.35 TOP: Parallel Lines and Transversals

200 ANS: 


KEY: grids 

201 ANS: 

ID: A 

The length of each side of quadrilateral is 5. Since each side is congruent, quadrilateral 

MATH is a rhombus. The slope of MH is 0 and the slope of HT is − 4 

. Since the slopes are not negative 

3 

reciprocals, the sides are not perpendicular and do not form rights angles. Since adjacent sides are not 

perpendicular, quadrilateral MATH is not a square. 

PTS: 6 REF: 011138ge STA: G.G.69 TOP: Quadrilaterals in the Coordinate Plane 

202 ANS: 4 

4(x + 4) = 8 2 

4x + 16 = 64 

4x = 48 

x = 12 

PTS: 2 REF: 061117ge STA: G.G.53 TOP: Segments Intercepted by Circle 

KEY: tangent and secant

203 ANS: 1 

x 2 = 7(16 − 7) 

x 2 = 63 

x = 9 7 

x = 3 7 


KEY: altitude 



205 ANS: 

x 2 = 9 ⋅ 8 

x = 72 

x = 36 2 

x = 6 2 


KEY: two chords 




TOP: Segments Intercepted by Circle KEY: two tangents 


TOP: Interior and Exterior Angles of Triangles 



210 ANS: 1 



TOP: Isosceles Triangle Theorem 

ID: A

212 ANS: 3 

5 10 

= 

7 x 

5x = 70 

x = 14 

PTS: 2 

213 ANS: 4 

REF: 081103ge STA: G.G.46 TOP: Side Splitter Theorem 

x + 6y = 12 

3(x − 2) = −y − 4 

6y = −x + 12 

y = − 1 

x + 2 

6 

m = − 1 

6 

−3(x − 2) = y + 4 

m = −3 




215 ANS: 


216 ANS: 3 


KEY: two tangents 


KEY: Centroid, Orthocenter, Incenter and Circumcenter 

ID: A

218 ANS: 3 

7x = 5x + 30 

2x = 30 

x = 15 


219 ANS: 



TOP: Triangles in the Coordinate Plane 

221 ANS: 2 

V = 4 

3 π r 3 = 4 

3 

 

6 

π ⋅ 

2 

3 

≈ 36π 


222 ANS: 3 

ID: A 


223 ANS: 


224 ANS: 

V = πr 2 h = π(5) 2 ⋅ 7 = 175π 



TOP: Properties of Transformations

226 ANS: 

x(x + 2) = 12 ⋅ 2. 

RT = 6 + 4 = 10. y ⋅ y = 18 ⋅ 8 

x 2 + 2x − 24 = 0 

(x + 6)(x − 4) = 0 

x = 4 

y 2 = 144 

y = 12 


KEY: tangent and secant 

ID: A


Answer Section 

227 ANS: 

18. If the ratio of TA to AC is 1:3, the ratio of TE to ES is also 1:3. x + 3x = 24. 

3(6) = 18. 

x = 6 

PTS: 4 REF: 060935ge STA: G.G.50 TOP: Tangents 

KEY: common tangency 

228 ANS: 1 

x + 2x + 2 + 3x + 4 = 180 

6x + 6 = 180 

x = 29 

ID: A 



TOP: Planes 

230 ANS: 2 

∠ACB and ∠ECD are congruent vertical angles and ∠CAB ≅ ∠CED. 

PTS: 2 REF: 060917ge STA: G.G.44 TOP: Similarity Proofs

231 ANS: 

ID: A 


232 ANS: 

Contrapositive-If two angles of a triangle are not congruent, the sides opposite those angles are not congruent. 

PTS: 2 REF: fall0834ge STA: G.G.26 TOP: Conditional Statements 

233 ANS: 2 

The slope of y = 1 

2 

1 

x + 5 is . The slope of a perpendicular line is −2. y = mx + b . 

2 

5 = (−2)(−2) + b 


234 ANS: 4 

TOP: Solids 

235 ANS: 2 


The slope of a line in standard form is − A 

−2 

, so the slope of this line is = 2. A parallel line would also have a 

B −1 

slope of 2. Since the answers are in slope intercept form, find the y-intercept: y = mx + b 

−11 = 2(−3) + b 

−5 = b 

PTS: 2 

236 ANS: 

180 − 46 

67. = 67 

2 

REF: fall0812ge STA: G.G.65 TOP: Parallel and Perpendicular Lines 


237 ANS: 4 

b = 1 

PTS: 2 REF: 081001ge STA: G.G.29 TOP: Triangle Congruency

238 ANS: 

y = −2x + 14. The slope of 2x + y = 3 is −A 

B 

= −2 

1 

= −2. y = mx + b 

4 = (−2)(5) + b 

b = 14 

PTS: 2 

239 ANS: 3 

36 + 20 

= 28 

2 




240 ANS: 




242 ANS: 3 PTS: 2 REF: fall0814ge STA: G.G.73 


243 ANS: 4 

(n − 2)180 = (8 − 2)180 = 1080. 1080 

= 135. 

8 

. 

ID: A 

PTS: 2 

244 ANS: 2 

REF: fall0827ge STA: G.G.37 TOP: Interior and Exterior Angles of Polygons 

3x + 5 + x − 1 

M x = = 

2 

4x + 4 

3y + (−y) 

= 2x + 2. M Y = = 

2 

2 

2y 

= y. 

2 


KEY: general

245 ANS: 

ID: A 

PTS: 2 REF: fall0830ge STA: G.G.55 TOP: Properties of Transformations 

246 ANS: 

AC ≅ EC and DC ≅ BC because of the definition of midpoint. ∠ACB ≅ ∠ECD because of vertical angles. 

ABC ≅ EDC because of SAS. ∠CDE ≅ ∠CBA because of CPCTC. BD is a transversal intersecting AB and 

ED. Therefore AB DE because ∠CDE and ∠CBA are congruent alternate interior angles. 

PTS: 6 REF: 060938ge STA: G.G.27 TOP: Triangle Proofs 

247 ANS: 2 


248 ANS: 3 

(x + 3) 2 − 4 = 2x + 5 

x 2 + 6x + 9 − 4 = 2x + 5 

x 2 + 4x = 0 

x(x + 4) = 0 

x = 0,−4 



TOP: Properties of Transformations



251 ANS: 

36, because a dilation does not affect angle measure. 10, because a dilation does affect distance. 


252 ANS: 

A″(8,2), B″(2,0), C ″(6,−8) 




254 ANS: 

y = 4 

3 x − 6. M −1 + 7 

x = = 3 

2 

M y = 

m = 

y − y M = m(x − x M ) . 

y − 1 = 4 

(x − 2) 

3 

1 + (−5) 

2 

1 − (−5) 

−1 − 7 

= −2 

= −3 

4 

The perpendicular bisector goes through (3,−2) and has a slope of 4 

3 . 

PTS: 4 REF: 080935ge STA: G.G.68 TOP: Perpendicular Bisector 

255 ANS: 

37. Since DE is a midsegment, AC = 14. 10 + 13 + 14 = 37 


ID: A

256 ANS: 

34. 2x − 12 + x + 90 = 180 

3x + 78 = 90 

3x = 102 

x = 34 

ID: A 


257 ANS: 

True. The first statement is true and the second statement is false. In a disjunction, if either statement is true, the 

disjunction is true. 

PTS: 2 

KEY: disjunction 

258 ANS: 2 

REF: 060933ge STA: G.G.25 TOP: Compound Statements 

140 − RS 

2 

= 40 

140 − RS = 80 

RS = 60 


KEY: outside circle 

259 ANS: 4 

The slope of y = − 2 

3 

x − 5 is −2 . Perpendicular lines have slope that are opposite reciprocals. 

3 


260 ANS: 

PTS: 4 REF: fall0835ge STA: G.G.42 TOP: Midsegments

261 ANS: 4 

Let AD = x. 36x = 12 2 

x = 4 

PTS: 2 

KEY: leg 

REF: 080922ge STA: G.G.47 TOP: Similarity 



263 ANS: 2 

Parallel chords intercept congruent arcs. mAD = mBC = 60. m∠CDB = 1 

mBC = 30. 

2 

ID: A 


264 ANS: 3 

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. 

PTS: 2 REF: fall0811ge STA: G.G.49 TOP: Chords 

265 ANS: 1 




TOP: Locus 


TOP: Planes 


TOP: Conditional Statements 

269 ANS: 3 




271 ANS: 

2.4. 5a = 4 2 

5b = 3 

a = 3.2 

2 

h 

b = 1.8 

2 = ab 

h 2 = 3.2 ⋅ 1.8 

h = 5.76 = 2.4 


KEY: altitude

272 ANS: 


273 ANS: 



TOP: Special Quadrilaterals 

275 ANS: 2 

87 + 35 

2 

= 122 

2 

= 61 




TOP: Planes 



278 ANS: 1 

V = πr 2 h 

1000 = πr 2 ⋅ 8 

r 2 = 1000 

8π 

r ≈ 6.3 



TOP: Solids 

ID: A

280 ANS: 

70. 3x + 5 + 3x + 5 + 2x + 2x = 180 

10x + 10 = 360 

10x = 350 

x = 35 

2x = 70 


281 ANS: 

15 + 5 5. 

PTS: 4 REF: 060936ge STA: G.G.69 TOP: Triangles in the Coordinate Plane 


TOP: Contrapositive 

283 ANS: 2 

PTS: 2 REF: 061026GE STA: G.G.51 TOP: Arcs Determined by Angles 


284 ANS: 4 

Median BF bisects AC so that CF ≅ FA. 

PTS: 2 REF: fall0810ge STA: G.G.24 TOP: Statements 

ID: A

285 ANS: 

8x − 5 = 3x + 30. 

4z − 8 = 3z. 

9y + 8 + 5y − 2 = 90. 

5x = 35 

x = 7 

z = 8 

14y + 6 = 90 

14y = 84 

y = 6 

PTS: 6 REF: 061038ge STA: G.G.39 TOP: Special Parallelograms 




TOP: Planes 

288 ANS: 

y = 2 

A −2 

x − 9. The slope of 2x − 3y = 11 is − = 

3 B −3 

= 2 

3 

 

2 

. −5 = (6) + b 

3 

−5 = 4 + b 

b = −9 


289 ANS: 

4. l 1 w 1 h 1 = l 2 w 2 h 2 

10 × 2 × h = 5 × w 2 × h 

20 = 5w 2 

w 2 = 4 



TOP: Planes 

ID: A

291 ANS: 

PTS: 2 REF: 061032ge STA: G.G.54 TOP: Reflections 

KEY: grids 

292 ANS: 

375π L = π r l = π(15)(25) = 375π 

PTS: 2 REF: 081030ge STA: G.G.15 TOP: Lateral Area 

293 ANS: 1 

y = x 2 − 4x = (4) 2 − 4(4) = 0. (4,0) is the only intersection. 


294 ANS: 

ID: A 

Because AB DC , AD ≅ BC since parallel chords intersect congruent arcs. ∠BDC ≅ ∠ACD because inscribed 

angles that intercept congruent arcs are congruent. AD ≅ BC since congruent chords intersect congruent arcs. 

DC ≅ CD because of the reflexive property. Therefore, ACD ≅ BDC because of SAS. 

PTS: 6 REF: fall0838ge STA: G.G.27 TOP: Circle Proofs 

295 ANS: 

452. SA = 4πr 2 = 4π ⋅ 6 2 = 144π ≈ 452 



TOP: Planes

297 ANS: 

110. 6x + 20 = x + 40 + 4x − 5 

6x + 20 = 5x + 35 

x = 15 

6((15) + 20 = 110 

ID: A 

PTS: 2 

298 ANS: 

REF: 081031ge STA: G.G.32 TOP: Exterior Angle Theorem 

Yes, m∠ABD = m∠BDC = 44 180 − (93 + 43) = 44 x + 19 + 2x + 6 + 3x + 5 = 180. 

Because alternate interior 

angles ∠ABD and ∠CDB are congruent, AB is parallel to DC . 

6x + 30 = 180 

6x = 150 

x = 25 

x + 19 = 44 

PTS: 4 

299 ANS: 1 

REF: 081035ge STA: G.G.35 TOP: Parallel Lines and Transversals 

Opposite sides of a parallelogram are congruent. 4x − 3 = x + 3. 

SV = (2) + 3 = 5. 

3x = 6 

x = 2 

PTS: 2 REF: 011013ge STA: G.G.38 TOP: Parallelograms 

300 ANS: 4 

x 2 = (4 + 5) × 4 

x 2 = 36 

x = 6 



301 ANS: 


KEY: grids 



303 ANS: 4 

180 − (50 + 30) = 100 


KEY: basic 

304 ANS: 4 

Corresponding angles of similar triangles are congruent. 

PTS: 2 REF: fall0826ge STA: G.G.45 TOP: Similarity 

KEY: perimeter and area 

305 ANS: 2 

Adjacent sides of a rectangle are perpendicular and have opposite and reciprocal slopes. 

ID: A 




307 ANS: 2 

2 + (−4) 

M x = 

2 

= −1. M Y = 

−3 + 6 

2 

= 3 

2 . 

PTS: 2 REF: fall0813ge STA: G.G.66 TOP: Midpoint 

KEY: general 



309 ANS: 1 

Translations and reflections do not affect distance. 


TOP: Analytical Representations of Transformations



311 ANS: 3 

. The sum of the interior angles of a pentagon is (5 − 2)180 = 540. 

ID: A 

PTS: 2 

312 ANS: 2 

3 6 

= 

7 x 


3x = 42 

x = 14 




314 ANS: 2 

(d + 4)4 = 12(6) 

4d + 16 = 72 

d = 14 

r = 7 


KEY: two secants 

315 ANS: 1 

The centroid divides each median into segments whose lengths are in the ratio 2 : 1. GC = 2FG 


GC + FG = 24 

2FG + FG = 24 

3FG = 24 

FG = 8

316 ANS: 

ID: A 

AB CD and AD CB because their slopes are equal. ABCD is a parallelogram 

because opposite side are parallel. AB ≠ BC . ABCD is not a rhombus because all sides are not equal. 

AB ∼ ⊥ BC because their slopes are not opposite reciprocals. ABCD is not a rectangle because ∠ABC is not a 

right angle. 


317 ANS: 4 

L = 2πrh = 2π ⋅ 5 ⋅ 11 ≈ 345.6 

PTS: 2 

318 ANS: 2 


−2 + 6 −4 + 2 

M x = = 2. M y = = −1 

2 

2 


KEY: general 

319 ANS: 1 

In an equilateral triangle, each interior angle is 60° and each exterior angle is 120° (180° - 120°). The sum of the 

three interior angles is 180° and the sum of the three exterior angles is 360°. 


320 ANS: 



TOP: Tangents KEY: common tangency

322 ANS: 1 

A′(2,4) 

PTS: 2 

KEY: basic 

REF: 011023ge STA: G.G.54 TOP: Compositions of Transformations 



324 ANS: 4 

SA = 4π r 2 

144π = 4π r 2 

V = 4 

3 π r 3 = 4 

3 π ⋅ 63 = 288π 

36 = r 2 

6 = r 


325 ANS: 

ID: A 

FE ≅ FE (Reflexive Property); AE − FE ≅ FC − EF (Line Segment Subtraction 

Theorem); AF ≅ CE (Substitution); ∠BFA ≅ ∠DEC (All right angles are congruent); BFA ≅ DEC (AAS); 

AB ≅ CD and BF ≅ DE (CPCTC); ∠BFC ≅ ∠DEA (All right angles are congruent); BFC ≅ DEA (SAS); 

AD ≅ CB (CPCTC); ABCD is a parallelogram (opposite sides of quadrilateral ABCD are congruent) 

PTS: 6 

326 ANS: 4 

REF: 080938ge STA: G.G.41 TOP: Special Quadrilaterals 

3y + 1 = 6x + 4. 

2y + 1 = x − 9 

3y = 6x + 3 

y = 2x + 1 

2y = x − 10 

y = 1 

x − 5 

2 

PTS: 2 REF: fall0822ge STA: G.G.63 TOP: Parallel and Perpendicular Lines

327 ANS: 1 

4x = 6 ⋅ 10 

x = 15 



328 ANS: 1 

(n − 2)180 

∠A = = 

n 

(5 − 2)180 

5 

= 108 ∠AEB = 

180 − 108 

2 

= 36 

ID: A 

PTS: 2 

329 ANS: 


2016. V = 1 1 

Bh = 

3 3 s2 h = 1 

3 122 ⋅ 42 = 2016 


330 ANS: 

25. d = (−3 − 4) 2 + (1 − 25) 2 = 49 + 576 = 625 = 25. 

PTS: 2 REF: fall0831ge STA: G.G.67 TOP: Distance 

KEY: general 


TOP: Parallel Lines and Transversals 



333 ANS: 1 

a 2 + (5 2) 2 = (2 15) 2 

a 2 + (25 × 2) = 4 × 15 

a 2 + 50 = 60 

a 2 = 10 

a = 10 

PTS: 2 REF: 011016ge STA: G.G.48 TOP: Pythagorean Theorem

334 ANS: 4 

d = (−3 − 1) 2 + (2 − 0) 2 = 16 + 4 = 20 = 4 ⋅ 5 = 2 5 


KEY: general 


TOP: Conditional Statements 

336 ANS: 2 

Parallel chords intercept congruent arcs. mAC = mBD = 30. 180 − 30 − 30 = 120. 

PTS: 2 

337 ANS: 3 


The slope of y = x + 2 is 1. The slope of y − x = −1 is −A −(−1) 

= = 1. 

B 1 

ID: A 


338 ANS: 1 

After the translation, the coordinates are A′(−1,5) and B′(3,4). After the dilation, the coordinates are A″(−2,10) 

and B″(6,8). 

PTS: 2 REF: fall0823ge STA: G.G.58 TOP: Compositions of Transformations 

339 ANS: 3 

4(x + 4) = 8 2 

4x + 16 = 64 

x = 12 


KEY: tangent and secant 



341 ANS: 4 

Longest side of a triangle is opposite the largest angle. Shortest side is opposite the smallest angle. 


342 ANS: 2 

x 2 = 3(x + 18) 

x 2 − 3x − 54 = 0 

(x − 9)(x + 6) = 0 

x = 9 

PTS: 2 REF: fall0817ge STA: G.G.53 TOP: Segments Intercepted by Circle 


343 ANS: 3 

2y = −6x + 8 

y = −3x + 4 

m = −3 

m ⊥ = 1 

3 

Perpendicular lines have slope the opposite and reciprocal of each other. 


344 ANS: 

BD ≅ DB (Reflexive Property); ABD ≅ CDB (SSS); ∠BDC ≅ ∠ABD (CPCTC). 

PTS: 4 REF: 061035ge STA: G.G.27 TOP: Quadrilateral Proofs 


TOP: Converse and Biconditional 

346 ANS: 

(6,−4). C x = Q x + R x 

2 

3.5 = 1 + R x 

2 

7 = 1 + R x 

6 = R x 

. C y = Q y + R y 

2 

8 + R y 

2 = 

2 

4 = 8 + R y 

−4 = R y 

PTS: 2 

KEY: graph 

347 ANS: 2 

REF: 011031ge STA: G.G.66 TOP: Midpoint 

y + 1 

x = 4 

2 

3x + 6y = 12 

y = − 1 

x + 4 

2 

m = − 1 

2 

6y = −3x + 12 

y = − 3 

x + 2 

6 

y = − 1 

x + 2 

2 

. 


ID: A

348 ANS: 3 

ID: A 

PTS: 2 

349 ANS: 1 

REF: 060902ge STA: G.G.28 TOP: Triangle Congruency 

−2 + 6 3 + 3 

M x = = 2. M y = = 3. The center is (2,3). d = 

2 

2 

(−2 − 6) 2 + (3 − 3) 2 is 8, the radius is 4 and r 

= 64 + 0 = 8. If the diameter 

2 = 16. 

PTS: 2 

350 ANS: 4 

REF: fall0820ge STA: G.G.71 TOP: Equations of Circles 


−4 

, so the slope of this line is = −2. A parallel line would also have a 

B 2 

slope of −2. Since the answers are in slope intercept form, find the y-intercept: y = mx + b 

3 = −2(7) + b 

17 = b 


351 ANS: 4 

(4) is not true if ∠PQR is obtuse. 


352 ANS: 1 

If ∠A is at minimum (50°) and ∠B is at minimum (90°), ∠C is at maximum of 40° (180° - (50° + 90°)). If ∠A is 

at maximum (60°) and ∠B is at maximum (100°), ∠C is at minimum of 20° (180° - (60° + 100°)). 


353 ANS: 1 

AB = 10 since ABC is a 6-8-10 triangle. 6 2 = 10x 

3.6 = x 


KEY: leg 



355 ANS: 

6. The centroid divides each median into segments whose lengths are in the ratio 2 : 1. TD = 6 and DB = 3 

PTS: 2 REF: 011034ge STA: G.G.43 TOP: Centroid

356 ANS: 

AC. m∠BCA = 63 and m∠ABC = 80. AC is the longest side as it is opposite the largest angle. 


357 ANS: 1 


358 ANS: 2 

x 2 + (x + 7) 2 = 13 2 

x 2 + x 2 + 7x + 7x + 49 = 169 

2x 2 + 14x − 120 = 0 

x 2 + 7x − 60 = 0 

(x + 12)(x − 5) = 0 

x = 5 

2x = 10 


359 ANS: 

PTS: 4 REF: fall0837ge STA: G.G.23 TOP: Locus 


TOP: Trapezoids 

ID: A

361 ANS: 2 

7 + 18 > 6 + 12 

PTS: 2 REF: fall0819ge STA: G.G.33 TOP: Triangle Inequality Theorem 







365 ANS: 1 

Since AC ≅ BC , m∠A = m∠B under the Isosceles Triangle Theorem. 

PTS: 2 REF: fall0809ge STA: G.G.69 TOP: Triangles in the Coordinate Plane 

366 ANS: 3 

V = πr 2 h = π ⋅ 6 2 ⋅ 27 = 972π 


367 ANS: 4 

d = (−6 − 2) 2 + (4 − (−5)) 2 = 64 + 81 = 145 

ID: A 


KEY: general 




TOP: Angle Side Relationship 

370 ANS: 4 

The marked 60º angle and the angle above it are on the same straight line and supplementary. This unmarked 

supplementary angle is 120º. Because the unmarked 120º angle and the marked 120º angle are alternate exterior 

angles and congruent, d e. 


371 ANS: 

5. 3 

x 

= 6 + 3 

15 

9x = 45 

x = 5 



TOP: Planes

373 ANS: 

2 3. x 2 = 3 ⋅ 4 

x = 12 = 2 3 

PTS: 2 REF: fall0829ge STA: G.G.47 TOP: Similarity 

KEY: altitude 

374 ANS: 4 

BG is also an angle bisector since it intersects the concurrence of CD and AE 


KEY: Centroid, Orthocenter, Incenter and Circumcenter 

375 ANS: 2 

A dilation affects distance, not angle measure. 

PTS: 2 REF: 080906ge STA: G.G.60 TOP: Identifying Transformations 

376 ANS: 4 

180 − (40 + 40) = 100 

PTS: 2 

377 ANS: 

REF: 080903ge STA: G.G.31 TOP: Isosceles Triangle Theorem 

18. V = 1 1 

Bh = 

3 3 lwh 

288 = 1 

⋅ 8 ⋅ 6 ⋅ h 

3 

288 = 16h 

18 = h 


378 ANS: 4 

The radius is 4. r 2 = 16. 

PTS: 2 

379 ANS: 3 

REF: 061014ge STA: G.G.72 TOP: Equations of Circles 

The diagonals of an isosceles trapezoid are congruent. 5x + 3 = 11x − 5. 

6x = 18 

x = 3 

PTS: 2 REF: fall0801ge STA: G.G.40 TOP: Trapezoids 

ID: A

380 ANS: 


381 ANS: 3 

m = −A 

B 

= −3 

4 



TOP: Planes 


TOP: Analytical Representations of Transformations 

384 ANS: 2 

4(4x − 3) = 3(2x + 8) 

16x − 12 = 6x + 24 

10x = 36 

x = 3.6 



385 ANS: 1 

3x 2 + 18x + 24 

3(x 2 + 6x + 8) 

3(x + 4)(x + 2) 

PTS: 2 REF: fall0815ge STA: G.G.12 TOP: Volume 



ID: A

387 ANS: 

PTS: 2 REF: fall0832ge STA: G.G.17 TOP: Constructions 



389 ANS: 

3. The non-parallel sides of an isosceles trapezoid are congruent. 2x + 5 = 3x + 2 

x = 3 


390 ANS: 

(x + 1) 2 + (y − 2) 2 = 36 

PTS: 2 

391 ANS: 4 

REF: 081034ge STA: G.G.72 TOP: Equations of Circles 

The slope of y = −3x + 2 is −3. The perpendicular slope is 1 1 

. −1 = (3) + b 

3 3 

−1 = 1 + b 

b = −2 







TOP: Tangents KEY: two tangents 



396 ANS: 4 

d = (146 − (−4)) 2 + (52 − 2) 2 = 25,000 ≈ 158.1 


KEY: general 



ID: A

398 ANS: 1 

−2 − 1 

 

y = 6x + 10 

 

2 

 

y = −12x − 20 


399 ANS: 1 

The closer a chord is to the center of a circle, the longer the chord. 


400 ANS: 3 

36 − 20 

= 8. 17 

2 

2 − 8 2 = 15 


401 ANS: 

y = 2 

x + 1. 2y + 3x = 6 

3 

2y = −3x + 6 

y = − 3 

x + 3 

2 

m = − 3 

2 

m⊥ = 2 

3 

. y = mx + b 

5 = 2 

(6) + b 

3 

5 = 4 + b 

1 = b 

y = 2 

x + 1 

3 



TOP: Tangents 

403 ANS: 2 

KEY: common tangency 

Because the triangles are similar, m∠A 

= 1 

m∠D 


KEY: perimeter and area 

ID: A

404 ANS: 

20. 5x + 10 = 4x + 30 

x = 20 


KEY: basic 

405 ANS: 1 

d = (−4 − 2) 2 + (5 − (−5)) 2 = 36 + 100 = 136 = 4 ⋅ 34 = 2 34 . 


KEY: general 



407 ANS: 4 

ABC ∼ DBE. AB 

DB 

= AC 

DE 

9 x 

= 

2 3 

x = 13.5 




409 ANS: 3 



TOP: Planes 

ID: A

411 ANS: 






414 ANS: 4 

y + x = 4 

y = −x + 4 

. x 2 − 6x + 10 = −x + 4. 

y + x = 4. 

y + 2 = 4 

x 2 − 5x + 6 = 0 

(x − 3)(x − 2) = 0 

x = 3 or 2 

y + 3 = 4 

y = 1 

PTS: 2 

415 ANS: 4 

REF: 080912ge STA: G.G.70 TOP: Quadratic-Linear Systems 

−6 + 1 

M x = = − 

2 

5 

2 . M 1 + 8 

y = = 

2 

9 

2 . 

y = 2 


KEY: graph 

416 ANS: 1 

PRT and SRQ share ∠R and it is given that ∠RPT ≅ ∠RSQ. 

PTS: 2 REF: fall0821ge STA: G.G.44 TOP: Similarity Proofs 

ID: A

417 ANS: 




419 ANS: 2 

6 + 17 > 22 

PTS: 2 REF: 080916ge STA: G.G.33 TOP: Triangle Inequality Theorem 

420 ANS: 

−4 + 4 

Midpoint: , 

2 

2 + (−4) 

 

 

2 

 

 

= (0,−1). Distance: d = (−4 − 4)2 + (2 − (−4)) 2 r = 5 

= 100 = 10 

x 2 + (y + 1) 2 = 25 

r 2 = 25 

PTS: 4 REF: 061037ge STA: G.G.71 TOP: Equations of Circles 

421 ANS: 

20. The sides of the triangle formed by connecting the midpoints are half the sides of the original triangle. 

5 + 7 + 8 = 20. 


422 ANS: 2 


B 

the opposite and reciprocal of each other. 

so the slope of this line is −5 

3 

ID: A 

Perpendicular lines have slope that are 

PTS: 2 REF: fall0828ge STA: G.G.62 TOP: Parallel and Perpendicular Lines

423 ANS: 

PTS: 2 

424 ANS: 1 


V = 1 

3 πr 2 h = 1 

3 π ⋅ 42 ⋅ 12 ≈ 201 


425 ANS: 4 

sum of interior ∠s = sum of exterior ∠s 

 

(n − 2)180 = n 180 − 

 

(n − 2)180 

n 

180n − 360 = 180n − 180n + 360 

180n = 720 

n = 4 

 

 

ID: A 




427 ANS: 2 

The slope of 2x + 3y = 12 is − A 

B 

(2) becomes y = 3 

x + 3. 

2 

= − 2 

3 

3 

. The slope of a perpendicular line is . Rewritten in slope intercept form, 

2 



TOP: Similarity KEY: perimeter and area 

429 ANS: 3 

The lateral edges of a prism are parallel. 

PTS: 2 REF: fall0808ge STA: G.G.10 TOP: Solids 

430 ANS: 2 

Longest side of a triangle is opposite the largest angle. Shortest side is opposite the smallest angle. 

PTS: 2 REF: 060911ge STA: G.G.34 TOP: Angle Side Relationship

431 ANS: 

D′(−1,1), E ′(−1,5), G′(−4,5) 




433 ANS: 2 

The length of the midsegment of a trapezoid is the average of the lengths of its bases. 






436 ANS: 1 

3x + 15 + 2x − 1 = 6x + 2 

5x + 14 = 6x + 2 

x = 12 

x + 30 

2 

= 44. 

x + 30 = 88 

x = 58 


437 ANS: 

26. x + 3x + 5x − 54 = 180 

9x = 234 

x = 26 

ID: A 

PTS: 2 REF: 080933ge STA: G.G.30 TOP: Interior and Exterior Angles of Triangles

438 ANS: 2 

The centroid divides each median into segments whose lengths are in the ratio 2 : 1. 



TOP: Locus 

440 ANS: 

22.4. V = πr 2 h 

12566.4 = πr 2 ⋅ 8 

r 2 = 12566.4 

8π 

r ≈ 22.4 

PTS: 2 REF: fall0833ge STA: G.G.14 TOP: Volume 


TOP: Planes 

442 ANS: 3 

m = −A 

B 

5 −A 10 5 

= . m = = = 

2 B 4 2 



TOP: Planes 

444 ANS: 


ID: A

445 ANS: 

∠D, ∠G and 24° or ∠E, ∠F and 84°. mFE = 2 

× 360 = 48. Since the chords forming ∠D and ∠G are 

15 

intercepted by FE, their measure is 24°. mGD = 7 

× 360 = 168. Since the chords forming ∠E and ∠F are 

15 

intercepted by GD, their measure is 84°. 

ID: A 

PTS: 4 REF: fall0836ge STA: G.G.51 TOP: Arcs Determined by Angles 



TOP: Similarity Proofs 



448 ANS: 1 

∠DCB and ∠ADC are supplementary adjacent angles of a parallelogram. 180 − 120 = 60. ∠2 = 60 − 45 = 15. 

PTS: 2 REF: 080907ge STA: G.G.38 TOP: Parallelograms 

449 ANS: 1 

(x,y) → (x + 3,y + 1) 

PTS: 2 REF: fall0803ge STA: G.G.54 TOP: Translations 

450 ANS: 

JK ≅ LM because opposite sides of a parallelogram are congruent. LM ≅ LN because of the Isosceles Triangle 

Theorem. LM ≅ JM because of the transitive property. JKLM is a rhombus because all sides are congruent. 

PTS: 4 REF: 011036ge STA: G.G.41 TOP: Special Quadrilaterals 






TOP: Tangents KEY: point of tangency 



455 ANS: 3 

PTS: 2 REF: fall0805ge STA: G.G.70 TOP: Quadratic-Linear Systems

456 ANS: 


ID: A

Geometry Regents at Random Worksheets - JMap

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