Name
Class
Date
End-of-Course Assessment Selected Response
4. Find the volume of a cone with diameter
16 cm and height 12 cm.
Read each question. Then circle the letter(s) of the correct answer(s). There may be more than one correct response. 1. What value of x makes nFGH similar
to nMNP? P
12
9
G
15
A B C D
100.5 cm3 804.2 cm3 2412.7 cm3 3217.0 cm3
5. A railway club provides free train rides
F
H
A B C D
x
4
on their large circular tracks. There are two tracks. The distance from Track 1 to the center is 30 m. The distance between Track 1 and Track 2 is 5 m. How much farther is the train ride on Track 2 than Track 1?
N
M
3 3.75 5.3 27
Track 1 Track 2
2. Write an equation of a circle with center
(21, 2) passing through the point (2, 4). A B C D
(x 1 1)2 1 ( y 2 2)2 5 13 (x 2 1)2 1 ( y 1 2)2 5 13 (x 1 1)2 1 ( y 2 2)2 5 169 (x 2 1)2 1 ( y 1 2)2 5 169
A B C D
3. Which equation(s) can be used to find
the value of x?
15.7 m 31.4 m 78.5 m 157.1 m
6. Which theorem(s) can you use to prove
that the two triangles are congruent? 14
x
42!
A cos 488 5
x 14
B sin 428 5
x 14
C cos 428 5
14 x
D sin 488 5
x 14
A B C D
ASA AAS SSS SAS
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7. Choose all the ways you can correctly
10. Which equation(s) represent a line
name plane P.
that contains the point (28, 3) and is perpendicular to y 5 4x 2 7? A x 1 4y 5 4 B y 5 4x 2 20
S A
X
Y B
1 4 1 D y 5 2 x 1 35 4 C y52 x11
P T A B C D
Date
m
plane AYB plane AYX plane YBP plane YBX
11. Which statement(s) are true? C
8. Choose all angle pairs that are
B
congruent.
5
1 2 4 3
A
A B C D
6 8 7
cos A 5 sin B sin A 5 cos A sin A 5 cos B tan A 5 tan B
12. Which edges of the prism are parallel A B C D
to AD?
/1 and /5 /1 and /6 /2 and /8 /4 and /6
B
E
y
H
A BC B EF
8
D
6
C FG D DH
C
2
B
G
F
B', C', and D' respectively. Choose all of the true statements.
4
D
A
9. A dilation maps points B, C, and D onto
10
C
D!
C! B!
2
4
x 6
8
10
A CD || CrDr
1 2
B The scale factor is . C
BC BD 5 BrCr BrDr
D nBCD > nBrCrDr
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16. Find the area of the sector.
13. The map below shows a section of a
city. Which statement(s) are true? Oak St.
Broad St.
9 cm 80 !
Main St. Maple St.
A B C D
A Oak Street is perpendicular to
Main Street. B Broad Street is parallel to Oak Street. C Main Street is parallel to Maple Street. D Oak Street is perpendicular to Broad Street.
4π cm2 9π cm2 12π cm2 18π cm2
17. What are all of the correct ways to
describe why the triangles below are congruent?
14. Which shape is formed by a vertical
M
plane intersecting the cone below? [G.GMD.4, Lesson 11-1]
L
N P A ASA Congruence Theorem B A reflection of nMNP across MP is a
A B C D
rigid motion that maps nMNP onto nPLM . C A translation, followed by a reflection, and then another translation is a series of rigid motions that will map nMNP onto nPLM . D A rotation of nMLP about point M, followed by a translation is a series of rigid motions that maps nMLP onto nPNM .
circle trapezoid triangle parallelogram
15. A bar of silver is shaped like a
trapezoidal prism. The dimensions of the base are shown below. If the height of the bar is 12 cm, what is its volume to the nearest tenth?
18. What are all the possible coordinates for
1 point M such that SM 5 MT ? 2
20.3 cm
S
8.9 cm
!5 !4 !3 !2 !1
25 cm
A B C D
A B C D
325.3 cm3 2419 cm3 2670 cm3 3261.6 cm3
T 0
213 22 21 13
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1
2
3
4
5
Name
Class
22. LMNK is a parallelogram. What are
19. A lifeguard sits on the shore in a chair
the values of x and y?
that is 6 ft above the ground. She sees a swimmer at an angle of depression of 108. About how far away from shore is the swimmer? A B C D
Date
L
M 2y ! 3
x
P
6.1 ft 34.0 ft 34.6 ft 95.1 ft
y!3
3x " 8
K
is sufficient to show that a similarity transformation exists that maps nPQR tonPrQrRr?
23. If an angle of one triangle is congruent
to an angle of a second triangle, and the sides that include the two angles are proportional, then what is true about the two triangles?
R P P’ R’
Q’
x 5 4, y 5 4 x 5 5, y 5 2 x 5 9, y 5 3 x 5 8, y 5 11
A B C D
20. Which of the following statements
Q
N
A The triangles are similar. B The triangles are congruent. C The triangles are neither similar nor
A /P > /Prand /Q > /Qr B PR > PrRr
congruent.
PQ PrQr 5 QR QrRr D QP 5 QrPr and QR 5 QrRr
D There is not enough information to
C
make a determination. 24. Find the value of x to the nearest tenth.
21. Triangle ABC is reflected across line m.
8
Which statement(s) are true?
x! 5
A A’
B
A 32.0 B 38.7
C C’ m
A B C D
C 51.3 D 58
25. What is the length of PQ?
B’
P
ArCr is perpendicular to CrBr. AB 5 ArBr m/A 5 m/Ar CCr 5 BBr
4x!3
S
Q 5x"3
R A 24 B 27
C 30 D 32
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98
Name
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Constructed Response
Date
30. What are the vertices of
T ,3, 21. (nFGH)? Graph the image of nFGH .
In this section, show all your work in the space beneath each test item.
y
26. Write an equation of a line parallel to
4
1 y 5 x 1 3 that passes through (2, 5). 2
G
F
x
O !4
2
!2 !2
27. If sin F 5 F
H
!4
3 , what is cos G? 5
G
H
4
g
31. Construct AB that is perpendicular to
line m.
28. An environmental group is making signs
for an upcoming community recycling day. They want the signs to be equilateral triangles with heights of 35 in. How long in inches will each side of the signs be? Round your answer to the nearest tenth of an inch.
m B
32. Constructs /S congruent to /R. 29. Is D(n, X)(nXYZ) 5 nXrY rZr an
enlargement or a reduction? What is the scale factor n of the dilation?
Y’
Z’ R
3
Y
Z 3
X!"X
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33. Determine whether the parallelograms
36. Does the transformation appear to be a
are similar. If so, write a similarity statement and give the scale factor. If they are not similar, explain why. A
4
Date
rigid motion? Explain.
B
Preimage
E
10
Image
F 6
D C H
G
15
34. Which can has a greater volume?
37. The diagonals of a quadrilateral are
congruent and perpendicular. Identify the quadrilateral.
How much greater? Round your answer to the nearest cubic inch. 4.5 in. 6 in. 8 in.
38. A student says that if two sides and
6 in.
one angle of one triangle are congruent to any two sides and one angle of another triangle, then the two triangles are congruent. What mistake did the student make? Draw two triangles that show the student is incorrect.
B
A 35. The measure of /5 is 110.
Write each angle in the correct column. m p q
1 2 4 3
5 6 8 7
39. Draw and label the reflection of square
LMNP across line t. Then describe how you know that LMNP and its image are congruent in terms of rigid motions.
9 10 13 14 12 11 16 15
t
L Angles that are congruent to j5
Angles that are congruent to j8 M
P
N
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40. The coordinates of the vertices of nABC
Date
44. Rectangle ABCD has vertices A(3, 5),
B(5, 5), C(5, 1), and D(3, 1). What are the coordinates of the vertices of r(90°, O)(ABCD)?
are A(0, 0), B(6, 2) and C(2, 24). What are the coordinates of the vertices after 1 a dilation of , followed by a reflection 2 across the y-axis?
y
y x O
x O
45. Find the perimeter of nTAP with
vertices T(1, 4), A(4, 4), and P(3, 0) to the nearest tenth.
41. Draw the lines of symmetry and give the
angle(s) of rotation for the figure below.
y
A
4 T 2
x O
2 P 4
42. Describe the shape of the vertical and
horizontal cross-sections of the cylinder below.
46. Show that the circles are similar by
finding a scale factor and describing a similarity transformation that maps circle P to circle Q. b
a 43. Determine if there is a similarity
transformation that maps one figure onto another. If so, describe the transformation and write a similarity statement. If not, explain why.
P
47. How can you use a congruence
transformation to show that the figures are congruent?
J A
H
Q
K
I
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101
Name
Class
Date
52. Construct an equilateral triangle. Label
48. Annie will use two right triangles to
any congruent sides or angles.
make a square for a logo. The triangles have the same side lengths and angle measures. What must also be true about the triangles in order to guarantee that the opposite sides of the square are parallel? Explain.
53. The three sides of nRST are congruent
to the three sides of nXYZ. Describe a rigid motion that proves that the triangles are congruent. R
49. Find a congruence transformation that
maps nCDF to nHJK. 6
y
Z T
K
4 2
H
!4
!2
C
O
2
D
X Y
J x
!6
S
4
54. A diagram of a water tower is shown
6
below. How can you use a geometric model to find the volume of the water tank at the top of the tower? Find the approximate volume. Use 3.14 for π.
F !6
76 ft.
50. You can find the density of an object by
m using d 5 , where m is the mass of the V object in grams and V is the volume in milliliters. What is the density of a can of tomato sauce with diameter 10 cm, height 11.5 cm, and a mass of 822 grams? Use the conversion factor 1 cm3 = 1 mL.
51. Describe the transformations that map
96 ft.
55. Write a congruence statement relating
triangles in the figure below.
Figure 1 onto Figure 3.
R
p 3
m O
T 2
Z
S
1
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Extended Response In this section, show all your work in the space beneath each test item. 56. Write a two-column proof to prove the Vertical Angles Theorem.
Given: /1 and /3 are vertical angles. Prove: /1 > /3 1 3
2
57. Write a proof to show that the diagonals of a rectangle are congruent.
Given: Rectangle ABCD Prove: AC > BD y
B(0, b)
A O
C(a, b)
D(a, 0) x
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103
Name
Class g
Date
g
58. Given: DL ' GP, DL bisects GP
Prove: GD 5 PD D
G
P
L
59. Prove that the diagonals of a parallelogram bisect each other.
Given: ~ABCD Prove: AC and BD bisect each other at point E.
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60. The state of Colorado is shaped like a rectangle with an approximate width of 280 mi and
length of 380 mi. What is the population density of Colorado in people per square mile if the population is 5,116,800?
61. The figure shows a pyramid inscribed in a cube. The volume of the pyramid is
72 cm3. Use the diagram and explain the relationship between the volume of the cube and the volume of the pyramid.
6 cm
62. Quadrilateral ABDC is inscribed in a circle. Prove that m/A 1 m/D 5 180. B A D
C
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105
Name
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63. Write a two-column proof. g
g
Given: nXYZ with PQ 6 XZ Prove: X
ZQ XP 5 PY QY P
1
Y 3
4
Q 2
Z
64. Prove the Triangle Angle-Sum Theorem.
Given: nGHK Prove: m/G 1 m/H 1 m/K 5 180 G
H K
65. GMPA and GRJF are parallelograms. GRA is an equilateral triangle. Prove that
m/F 5 m/P. G
R A
F
M P
J
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