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Answers to Exercises 18. The golden ratio is 1+ 5 , or approximately 2 1.618. Here is one possible construction: A mB 90° Construct BC 1 2 AB AC 2 5 AB AX AD 2 5 AB 1 2 AB AX 5 1 2 AB AB 2 AX 5 1 1+ 2 5 Therefore, X is the golden cut. 128 ANSWERS TO EXERCISES D X C B 19a. Answers will vary. 19b. Possible answer: The shape is an irregular curve. 19c. Answers will vary. Possible answers: As the circular track becomes smaller, the curve becomes more circular; as the track becomes larger, the curve becomes more pointed near the fixed point. As the rod becomes shorter, the curve becomes more pointed near the fixed point; as the rod becomes longer, the curve becomes more like an oval. As the fixed point moves closer to the traced endpoint, the curve becomes more pointed near the fixed point; as the fixed point moves closer to the circular track, the curve begins to look like a crescent moon.
1. 18 cm 2. 12 cm 3. 21 cm 4. 15 cm 5. 2.0 cm 6. 126 cm2 ; 504 cm2 7. 16 cm 8. 60 cm 9. 4 4 9 cm p b 10. q ; q LESSON 11.4 11. 63 cm 12. 6 cm 13. x 3 1 3 cm, y 5 13 3 cm, z 8 2 3 cm 14. B (3, 5), R 13 4 ,7 ; k 7 h 4 15. 2 1 16. H L E O V M A Consider similar triangles LVE and MTH with corresponding angle bisectors EO and HA . To show that the corresponding angle bisectors are proportional to corresponding sides, for example EO EL HA , HM show by AA that LOE MAH, EO EL and then you can show that HA . HM You know that L M. Use algebra to show that LEO MHA. T 17. a b 1 c d 1 a b b b c d d d a b c d b d 18. The ratio will be the same as the ratio for the original rectangle. The ratio is 1 2 if it can be divided like this: It might be any ratio if divided like this: 19. Yes, by the SSS or the SAS Similarity Conjecture. 20a. 2a b 20b. 2a b 20c. all values of a and b 20d. no values of a and b 21. AB 3 cm, BC 7.5 cm ANSWERS TO EXERCISES 129 Answers to Exercises
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Answers to Exercises 0 CHAPTER 0
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LESSON 0.3 1. Design with reflectio
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LESSON 0.5 1. possible answers: Sco
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CHAPTER 0 REVIEW 1. possible answer
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USING YOUR ALGEBRA SKILLS 1 1. (3,
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34. B 35. MY; CK; mI 36. SEU; EUO;
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20. false 21. true 22. false; Thoug
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LESSON 1.5 1. D 2. A 3. C 4. B 5. C
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LESSON 1.7 1. Answers will vary. Sa
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LESSON 1.8 1. 2. 3. 4. 5. 6. 7. 8.
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CHAPTER 1 REVIEW 1. true 2. False;
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Answers to Exercises CHAPTER 2 •
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8. 8n is steeper; the coefficient o
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LESSON 2.4 1. inductive; deductive
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LESSON 2.6 1. 63° 2. 90° 3. no 4.
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CHAPTER 2 REVIEW 1. poor inductive
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1. 2. 3. 4. 5. A B Q D C D 1 CD 2 E
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1. LESSON 3.3 The answer depends on
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1. D 2. F 3. A 4. C 5. E 6. 7. 8. 9
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LESSON 3.5 1. 2. 3. Construct a seg
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LESSON 3.6 1. Sample description: C
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1. incenter LESSON 3.7 Because the
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LESSON 3.8 1. The center of gravity
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42. true 43. False; any non-acute t
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LESSON 4.2 1. 79° 2. 54° 3. 107.5
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1. yes 2. no 3. no 4 5 9 5 6 12 LES
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LESSON 4.5 1. If two angles and the
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1. See flowchart below. 2. See flow
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1. 6 2. 90°; 18° 3. 45° 4. See f
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CHAPTER 4 REVIEW 1. Their rigidity
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Answers to Exercises 5 CHAPTER 5
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LESSON 5.3 1. 64 cm 2. 21°; 146°
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1. 34 cm; 27 cm 2. 132°; 48° 3. 1
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1. 2. 3. (0, 4) y y y (0, 6) USING
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22. The platform stays parallel to
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7. 2 RE AB 3 BR EA 4 AR EB
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20. Speed: 901.4 km/h. Direction:
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LESSON 6.2 1. 165°, definition of
Page 77 and 78: 1 OR CD ? 5 OC OD ? All radii o
Page 79 and 80: LESSON 6.5 1. d 5 cm 2. C 10 cm 3
Page 81 and 82: 1. 1 2 ,3 USING YOUR ALGEBRA SKILL
Page 83 and 84: CHAPTER 6 REVIEW 1. Answers will va
Page 85 and 86: Answers to Exercises CHAPTER 7 •
Page 87 and 88: 15. possible answer: HIKED 16. one,
Page 89 and 90: LESSON 7.4 1. Answers will vary. 2.
Page 91 and 92: LESSON 7.6 1. Answers will vary. 2.
Page 93 and 94: 1. parallelograms 2. parallelograms
Page 95 and 96: CHAPTER 7 REVIEW 1. true 2. true 3.
Page 97 and 98: 1. 20 cm 2 2. 49.5 m 2 3. 300 squar
Page 99 and 100: USING YOUR ALGEBRA SKILLS 8 1. x 2
Page 101 and 102: LESSON 8.5 1. 9 in 2 2. 49 cm 2 3.
Page 103 and 104: LESSON 8.7 1. 150 cm 2 2. 4070 cm 2
Page 107 and 108: USING YOUR ALGEBRA SKILLS 9 1. 6 2.
Page 109 and 110: LESSON 9.4 1. No. The space diagona
Page 111 and 112: LESSON 9.6 1. 18 cm2 56.5 cm2 2. (
Page 113 and 114: 32. 4 in./s 12.6 in./s 33. true 34
Page 115 and 116: 36. See table below. Possible answe
Page 117 and 118: LESSON 10.3 1. 192 cm3 2. 84 cm3 2
Page 119 and 120: LESSON 10.5 1. 675 cm3 2. 36 cm3 1
Page 121 and 122: LESSON 10.7 1. V 972 cm3 3054 cm3
Page 123 and 124: CHAPTER 10 REVIEW 1. They have the
Page 125 and 126: 1. A 2. B 3. possible answer: 3. po
Page 127: LESSON 11.3 1. 16 m 2. 4 ft 3 in. 3
Page 131 and 132: 1. 1715 cm 3 LESSON 11.6 2. 16 cm,
Page 133 and 134: Use segment addition to show that e
Page 137 and 138: LESSON 12.3 1. 329 cm 2 2. 4 cm 2 3
Page 139 and 140: LESSON 12.5 1. approximately 12.7 m
Page 141 and 142: 13. f(x) 1 2 (x3)2 2; A vertical s
Page 145 and 146: LESSON 13.2 1. Linear Pair Postulat
Page 147 and 148: LESSON 13.3 1. Case 1: P is colline
Page 149 and 150: 1. A LESSON 13.4 Use x to represent
Page 151 and 152: LESSON 13.5 1. D: Paris is in Franc
Page 153 and 154: 8. Use the Inscribed Angle Theorem
Page 155 and 156: 11. CA Postulate 12. 13. Perpendicu
Page 157 and 158: 8. Task 1: Given: A rectangle with
Page 159 and 160: CHAPTER 13 REVIEW 1. False. The qua
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