CHAPTERS Cumulative Test 1–6 For use after Chapters 1–6 · PDF file · 2013-08-11Geometry 126 Chapter 6 Assessment Book ... 9 10 11 12 13 14 15 16 3 4 22. ∠ 4 and 14.....
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2. Name the intersection of plane ABDand plane AEB.
3. Are points B, C, and D collinear?
4. Are points E, A, and D coplanar?
5. Name two planes that intersect at line @##$ EC .
In Exercises 6 and 7, the endpoints of a segment are given. Find the length of the segment rounded to the nearest tenth. Then fi nd the coordinates of the midpoint of the segment.
6. A(23, 4) and B(1, 28) 7. F(26, 27) and G(5, 23)
Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular.
8. 9.
Use the information about the fi gure to fi nd the indicated measure.
10. Perimeter 5 46 m 11. Area 5 175 ft2 12. Perimeter 5 39 in. Find the length l. Find the height h. Find the side length s.
Decide whether enough information is given to prove that the triangles are congruent. If there is enough information, state the congruence postulate or theorem you would use.
46. A B
CD
47. G
H
J
F
48. P
Q
R
S
49. T
US
V
Find the values of x and y.
50.
1148
x 8
y 8 51. 688
(5x 1 3)8
4y 8
52.
(7x 1 12)8
Cumulative Test continuedFor use after Chapters 1–6
Find the unknown side length of the right triangle.
1.
x
99
20 2.
x
90
106 3. x 36
85
Find the value of each variable. Write your answers in simplest radical form.
4.
x
y
45810
5. x
y60825
6.
x
y
30818 3
7. You are measuring the height of a Ferris wheel at an amusement park. You are standing 125 feet from its base. You measure the angle of elevation from a point on the ground to the top of the Ferris wheel to be 518. Estimate the height of the Ferris wheel. Round your answer to the nearest foot.
Solve the right triangle. Round decimal answers to the nearest tenth.
8.
A C
B
558
12
9.
H G
F
678
25
10. R P20
17
Find the indicated measure.
11. m∠ PSQ 12. XV
P
RS
T
10
498
Y X
V
Z
W15
13. What are the measures of an interior angle and an exterior angle of a regular 30-gon?
17. ABCD has vertices A(25, 4), B(27, 1), C(25, 21) and D(23, 2), and EFGH has vertices E(3, 6), F(21, 0), G(3, 24), and H(7, 2). Tell whether the quadrilaterals are congruent, similar, or neither.
The vertices of n XYZ are X(21, 4), Y(3, 4), and Z(2, 1). Translate n XYZ using the given vector. Graph its image.
18. ⟨22, 0⟩ 19. ⟨1, 23⟩
Add, subtract, or multiply.
20. F 24 7 22 12G 1 F 3 21
25 210G 21. f8 26 4g 2 f27 2 23g
22. f9 5gF 24 6G 23. F 21 6
5 1GF 24 2 22 0G
Find the image matrix that represents the polygon after a refl ection in the given line.
24. x-axis 25. y 5 2x
Cumulative Test continuedFor use after Chapters 7–12
Cumulative Test continuedFor use after Chapters 7–12
The vertices of n STU are S(1, 22), T(5, 22), and U(1, 24). Find the coordinates of the image of n STU after a composition of the transformations in the order they are listed.
26. Translation: (x, y) → (x 2 1, y 1 4)Refl ection: in the y-axis
27. Translation: (x, y) → (x 2 3, y 2 1)Rotation: 908 about the origin
Decide whether the fi gure has line symmetry and/or rotational symmetry. Identify the number of lines of symmetry and/or the rotations that map the fi gure onto itself.
28. 29. 30.
Find the image matrix that represents a dilation of the polygon centered at the origin with the given scale factor.
A B C A B C
31. F 1 3 0 6 2 4G; k 5 2 32. F 28 24 28
4 4 0G; k 5 3 } 4
Find the value of each variable.
33. A
x8
928
BC
34. G
x 8
5y8888
1258
J
F
H
35.
x 8
648
488
J
M L
K
36.
(5x 2 1)8 (11x 1 9)8388
S
T
WV
U
Write the standard equation of the circle with the given center and radius.
37. Center (0, 23), radius 5 38. Center (22, 6), radius 1
39. Give an equation of a line that does not intersect the circle described by the equation (x 2 1)2 1 (y 1 2)2 5 64.
Find the surface area and volume of the fi gure. Round your answers to two decimal places, if necessary.
44. 12 cm
15 cm
45. 39 yd
89 yd
46. 11.6 m 47.32 in.
48 in.
48. Find the volume of the silo shown at the right. 20 ft
68 ft
Round your answer to two decimal places.
49. Two rectangular prisms have a scale factor of 3 : 4. The smaller rectangular prism has a surface area of 12,582 square meters. Find the surface area of the larger rectangular prism.
50. Two right cones have a scale factor of 1 : 5. The larger cone has a volume of 1875π cubic feet. Find the volume of the smaller cone.
Cumulative Test continuedFor use after Chapters 7–12
18. a. The 16 3 20 and the 20 3 30 both have a ratio of 1 : 40. b. The 16 3 20 is an enlargement by a scale factor of 2 of the 8 3 10. The 20 3 30 is an enlargement by a scale factor of 5 of the 4 3 6. c. 2 in. 3 3 in. d. Use a scale factor of
1 } 5
for a reduction of the 20 3 30, or use a scale fac-tor of 2 for an enlargement of the wallet size.
Standardized Test B
1. D 2. B 3. A 4. C 5. A 6. D 7. D
8. B 9. C 10. C 11. B 12. B 13. D
14. A 15. D 16. 195 17. length is 1 : 1, width is 1 : 16, area is 1 : 16; After 5 folds: length is 1 : 1, width is 1 : 32, area is 1 : 32; After 6 folds; length is 1 : 1, width is 1 : 64, area is 1 : 64
18. a. A, B, C, E b. The 16 3 20 is an enlargement dilation of the 8 3 10 by a scale factor of 2 : 1. The 10 3 14 is an enlargement dilation of the 5 3 7 by a scale factor of 2 : 1. The 4 3 6 is an enlargement dilation of the 2 3 3 by a scale factor of 2 : 1. The 12 3 16 is an enlargement dilation of the 1.5 3 2 by a scale factor of 8 : 1 c. C and E could print on a 10 3 14. G, I, and J could print on an 6 3 8.
Standardized Test C
1. D 2. B 3. D 4. A 5. D 6. B 7. D 8. A
9. C 10. D 11. B 12. D 13. C 14. C
15. C 16. 15.2 17. 9 ft by 33 ft; 297 ft2
18. a. The 5 3 7 has a ratio of 3 : 35.; The 16 3 20 and 30 3 40 both have a ratio of 1 : 40. b. The
4 3 6 is a reduction by a scale factor of 1 }
6 of the
24 3 36. The 8 3 10 is a reduction by a scale
factor of 1 }
2 of the 16 3 20. c. (10, 14) d. 1 }
5 ;
(3, 4.4)
SAT/ACT Chapter Test
1. B 2. C 3. D 4. A 5. E 6. D 7. D 8. C
9. B 10. B 11. A 12. 40 13. 5 ft
Performance Assessment
1. Complete answers should include:
C(6, 2)x
y
2
12
N(18, 6)L(6, 6)
A(2, 2)
F(3, 1)
E(2, 3)
B(4, 6)
D(1, 1)
M(12, 18)
AB
} DE 5 BC
} EF 5 AC
} DF 5 2, so n ABC , nDEF;
AB
} LM 5 BC
} MN 5 AC
} LN 5 1 }
3 , so n ABC , nLMN;
DE
} LM 5 EF
} MN 5 DF
} LN 5 1 }
6 , so nDEF , nLMN.
2. a. 12 ft by 8 ft b. Because ∠A and ∠C are right angles, ∠A > ∠C. By the Refl exive Property, ∠E > ∠E. So n ABE and nCDE are similar by the AA Similarity Postulate. c. 1.5
d. LF
} FB 5 LM
} ME e. Show that LJ
} LN = LH
} LI . Then
use the Refl exive Property and the SAS Similarity Theorem to show that the triangles are similar.
Chapters 1–6
Cumulative Test
1. point D 2. @##$ AB 3. no 4. yes 5. plane ECD and plane ECB 6. 12.6; (21, 22)
7. 11.7; 1 2 1 } 2 , 25 2 8. decagon, equilateral
9. quadrilateral, equilateral 10. 16 m
11. 12.5 ft 12. 9.75 in. 13. 12, 3, 0.75
14. 214, 224, 236 15. If you are not a politician, then you are not a senator.; true
19. a. 33,510.32 in.3 b. 4188.79 in.3; No, the volume is one-eighth the larger volume because
the ratio of the radii is 1 }
2 , making the ratio of the
volumes equal to 1 }
23 .
20. a. 7125.13 in.2 b. 45,804.42 in.3 c. 153 min d. 198 gal
Standardized Test B
1. C 2. A 3. D 4. B 5. A 6. C 7. B
8. B 9. A 10. D 11. B 12. B 13. A
14. A 15. D 16. C 17. D 18. 588 ft3
19. a. 4188.79 in.2 b. No; 523.60 in.3
20. a. 527.52 ft2 b. 904.78 ft3 c. 226.08 min
d. water: 646.27 ft3; syrup; 258.51 ft3
Standardized Test C
1. C 2. B 3. C 4. D 5. C 6. B 7. B
8. A 9. B 10. C 11. A 12. D 13. B
14. D 15. C 16. D 17. D 18. 620
19. a. 10,305.99 in.3 b. 161.03 in.3; No, the
volume is 1 }
64 the larger volume because the ratio
of the diameters is 1 }
4 , making the ratio of the
volumes equal to 1 }
43 .
20. a. 68.04 ft2 b. 38.61 ft3 c. 15 min d. 1092.6 L
SAT/ACT Chapter Test
1. A 2. D 3. B 4. C 5. C 6. D 7. C 8. B
9. B 10. C 11. E 12. 197 13. 10.8
Performance Assessment
1. Find the volume of a right prism or right cylinder by multiplying the area of the base by the height. Find the volume of a regular pyramid or right cone by fi nding one third of the product of the area of the base and the height. Find the area of a sphere by fi nding four thirds of the product of pi and the cube of the radius.
2. a. 15 ft3; 46 ft2 b. 13.5 ft2 c. about 1718.44 in.3 d. about 147.22 in.3; 170 in.2 e. Subtract the volume of the pyramid that is cut off from the main pyramid.