A1© 2015 College Board. All rights reserved. SpringBoard Course 3, Unit 3 Practice

LeSSon 16-1 1. a. 758; 1658

b. 538; 1438

c. 198; 1098

d. 278; 1178

e. (90 2 x)8; (180 2 x)8

2. a. 268; 648

b. 26.58; 63.58

c. 368; 548

d. 338; 578

e. 258; 658

3. a. 72.58; 107.58

b. 31.58; 148.58

c. 458; 1358

d. 598; 1218

e. 14.88; 165.28

4. Answers may vary. Check students’ answers.

5. C

LeSSon 16-2 6. Angle Measure

/RHC 1458

/JHK 1458

/RHJ 358

/CHK 358

/HKS 358

/SKU 1458

/OKU 358

/HKO 1458

7. a. 1808

b. Angles JHK and HKS are supplementary angles because the sum of the angle measures is 1808.

8. B

9. a. /1 and /3 are corresponding angles.

b. /2 and /8 are vertical angles.

c. /1 and /5 are alternate exterior angles.

d. /3 and /7 are alternate interior angles.

e. /3 and /6 are adjacent angle that form a straight line.

10. a. 628

b. x 5 24

LeSSon 17-1 11. a. 658

b. 418, 578, 828

12. a. 808

b. 508

c. 608

d. 508

e. 658

13. a. 508, 528, 788

b. 208, 458, 1158

c. 258, 658, 908

d. 368, 488, 968

e. 348, 618, 858

14. C

15. The measure of each base angle is 368.

Answers to Course 3 Unit 3 Practice

A2© 2015 College Board. All rights reserved. SpringBoard Course 3, Unit 3 Practice

LeSSon 17-2 16. a. 808

b. 358

c. 938

d. 728

e. 348

17. 1028, 1218, 1378; Students’ explanations may vary. Students may use the relationship between the two remote interior angles and the exterior angle as well as the sum of the angle measures of a triangle and the sum of the adjacent angles of a straight angle.

18. a. 908

b. 1008

c. 508, 1608

d. 808, 958

e. 708, 608

19. C

20. The sum of the two given angles is 155. Marion knows that the sum of the angle measures of a triangle is 180. She subtracts 180 2 155 5 25 to determine the third angle of the triangle. Bruce subtracted the sum from 360, 360 2 155 5 205. Three hundred sixty is the sum of the angle measures of a quadrilateral. Bruce is not correct.

LeSSon 18-1 21. reflection

22. rotation

23. translation

24. The transformation is a reflection where the line of reflection is the long leg of the right triangle.

25. B

LeSSon 18-2 26. a. Quadrilateral ABCD is translated right 8 units

and down 2 units.

b. (x, y) (x 1 8, y 2 2)

27. a. The figure translates down 3 units.

b. The figure translates right 5 units and up 1 unit.

c. The figure translates left 2 units.

d. The figure translates right 3 units and down 2 units.

28. a. G9(2, 7), E9(5, 3), O9(2, 3)

b. G9(23, 4), E9(0, 0), O9(23, 0)

c. G9(1, 3), E9(4, 21), O9(1, 21)

d. G9(24, 1), E9(21, 23), O9(24, 23)

e. G9(23, 0), E9(0, 24), O9(23, 24)

29. D

30.

x

y

212223242526 1

123456

2 3 4 5 6

LeSSon 18-3 31. a. y

A B

C

x

2

4

6

8

2 4 6 80A'

B' C'

A3© 2015 College Board. All rights reserved. SpringBoard Course 3, Unit 3 Practice

b. Coordinates of nABC Coordinates of nA9B9C9

A (1, 4) A9 (4, 1)

B (3, 4) B9 (4, 3)

C (3, 7) C9 (7, 3)

c. (x, y) (y, x)

32. A

33. J9(25, 2), K9(22, 2), L9(23, 5), M9(26, 5)

34. a. The line of reflection is the y-axis.

b. (x, y) (2x, y)

35. The x-coordinate stays the same when a figure is reflected over the x-axis.

LeSSon 18-4 36. a. (22, 23)

b. (3, 22)

c. (2, 3)

37. D

38. a. y

x

2

4

6

26

24

22

222426 2 4 60

GI

H

H'

G'I'

b. Coordinates of nGHI Coordinates of nG9H9I9

G (1, 3) G9 (21, 23)H (3, 22) H9 (23, 2)I (4, 2) I9 (24, 22)

c. (x, y) (2x, 2y)

39. a. R9(3, 24), S9(22, 21), and T 9(2, 3)

b. R9(3, 24), S9(22, 21), and T 9(2, 3)

c. A 2708 counterclockwise rotation is the same as a 908 clockwise rotation.

40. a. Triangle XYZ is rotated 908 counterclockwise about the origin.

b. (x, y) (2y, x)

LeSSon 19-1 41. a. y

xA C

BB'

A'

C'

b. Coordinates of nABC Coordinates of nA9B9C9

A (1, 1) A9 (21, 1)B (3, 4) B9 (24, 3)C (3, 1) C9 (21, 3)

c. Side AC and side A9C9 are both 2 units long. Side BC and side B9C9 are both 3 units long.

d. The area of nABC and the area of nA9B9C9 are both 3 square units.

e. The corresponding sides of the preimage and image are congruent. The areas are the same. nABC and nA9B9C9 are congruent.

A4© 2015 College Board. All rights reserved. SpringBoard Course 3, Unit 3 Practice

42. y

x

2

4

6

8

10

210

28

26

24

22

22242628210 2 4 6 8 100

J

L K

a.

b.

c.

d. All of the transformations are congruent to nJKL.

43. B

y

x

2

4

6

8

10

210

28

26

24

22

22242628210 2 4 6 8 100

J

L K

J'

L'K'

y

x

2

4

6

8

10

210

28

26

24

22

22242628210 2 4 6 8 100

J

K L

J''

L''K''

y

x

2

4

6

8

10

210

28

26

24

22

22242628210 2 4 6 8 100

J

K L

J'''

L'''K'''

A5© 2015 College Board. All rights reserved. SpringBoard Course 3, Unit 3 Practice

44. a. m

AA'

B'

C'

D'

B

C

D

b. side B9C9

c. /D9

d. The preimage and image are congruent because the corresponding sides and corresponding angles are congruent.

45. Translations, reflections, and rotations change the location of a figure but not the size of the figure.

LeSSon 19-2

46. K9(23, 25), K0(3, 25)

47. a. P9(2, 4), Q9(24, 6), R9(26, 3); P0(1, 7), Q0(25, 9), R0(23, 3)

b. P9(22, 7), Q9(28, 9), R9(26, 3); P0(22, 27), Q0(28, 29), R0(26, 23)

c. P9(6, 21), Q9(8, 27), R9(2, 25); P0(26, 21), Q0(28, 27), R0(22, 25)

d. P9(6, 1), Q9(8, 7), R9(2, 5); P0(6, 21), Q0(8, 27), R0(2, 25)

48. (x, y); The result is a 3608 rotation. The composition returns the figure to its original position on the coordinate plane.

49. D

50. a. y

x

2

4

6

26

24

22

222426 2 4 60

A

B'

B''

A''

B

C

b. (x, y) (y, 2x)

LeSSon 20-1 51. a. yes; The corresponding angles are congruent

and the corresponding sides are proportional. nABC | nRST.

b. yes; The corresponding angles are congruent and the corresponding sides are proportional. nGHK | nOMN.

52. a. m/P

b. PT

53. D

54. a. /C and /D, /A and /O, /T and /G

b. CA and DO, AT and OG, CT and DG

55. 156

, 208

, 2510

LeSSon 20-2 56. a. 708

b. 758

c. 358

d. 758

57. a. x 5 24 in., y 5 21 in.

b. x 5 10 ft, y 5 15 ft

c. x 5 24 cm, y 5 3 cm

A6© 2015 College Board. All rights reserved. SpringBoard Course 3, Unit 3 Practice

58. 212

ft

60. 24

LeSSon 21-1

61. a. 12

b. 12

c. 14

62. C

63. a. Check students’ work.y

x

2

4

6

8

10

12

210

212

28

26

24

22

22242628210 2 4 6 8 100

b. 56 square units

c. 224 square units

d. 41

64. The image is smaller than the preimage because the ratio of the perimeters is less than 1.

65. 43

; Find the square root of 169

.

LeSSon 21-2 66. B

67. a. 23

b. The dilation is a reduction because the scale factor is less than 1.

c. 49

68. a. 126 ft

b. 882 sq ft

69. 13

70. 1313

sq cm

LeSSon 22-1 71. B

72. D

73. 15 inches

74. 65 inches

75.

LeSSon 22-2 76. The second one because it is the only right

triangle.

77. 21.2 feet

78. 36 ft

79. 16 yd

80. 32.2 feet

Jon:82 1 122 5 c2

64 1 144 5 208208 5 14.4 mm

A7© 2015 College Board. All rights reserved. SpringBoard Course 3, Unit 3 Practice

LeSSon 23-1

81. B

82. 53 in.

83. 6 blocks

84. 45 in.

85. 197 mm

LeSSon 23-2 86. C

87. A

88. 4.5 units

89. 12 units

90. 14.1 units

91. 5.1 units

LeSSon 24-1 92. A

93. C

94. No, because 92 1 202 does not equal 402.

95. Yes, because 0.62 1 0.82 5 12.

96. No, because 0.92 1 1.12 does not equal 1.52.

LeSSon 24-2 97. 50

98. C

99. Answers will vary. Sample answer: 10, 24, 26; 15, 36, 39; 20, 48, 52

100. Always, because the operations of multiplication maintains proportionality.

101. Never, because the operations of addition does not maintain proportionality.

102. Sometimes, because Pythagorean triples can only be created from right triangles.

LeSSon 25-1 103. LA: 156 m2 SA: 172 m2

104. LA: 102.24 cm2 SA: 106.08 cm2

105. LA: 1620 in.2 SA: 1815 in.2

106. 528 ft2

107. 36 in.2

LeSSon 25-2 108. 2042 ft2

109. A

110. C

111. False, the height of the cylinder is needed.

A8© 2015 College Board. All rights reserved. SpringBoard Course 3, Unit 3 Practice

112. True, the diameter can be used to find the circumference, which is then multiplied by the height.

LeSSon 26-1 113. 437.25 ft3

114. 160 in.3

115. 1,380,448.3 m3

116. D

117. C

LeSSon 26-2 118. 127.2 in.3

119. 11317

ft3

120. D

121. Kim is correct because 22(3.14)(9)3

5 37.68.

122. 3052.08 ft3

LeSSon 26-3 123. 48 mm3

124.

125. 83.8 in.3

126. B