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<strong>Answers</strong> to Exercises 11. A 2 1 D 4 3 Use the Parallelogram Opposite Angles Theorem, the multiplication property, and the definition of angle bisector to get 1 3. Then use the Converse of the Isosceles Triangle Theorem, the definition of isosceles triangle, and the Parallelogram Opposite Sides Theorem to get AB BC DC AD . 12. W Z X P Y Use the Converse of the Angle Bisector Theorem to prove that WY is the angle bisector of Y. In like manner, WY is the angle bisector of W. Therefore, WXYZ is a rhombus by the Converse of the Rhombus Angles Theorem. 13. Linear Pair Postulate CA Postulate Interior Supplements Theorem Parallelogram Consec. Angle Theorem 150 ANSWERS TO EXERCISES B C Q 17. (Lesson 13.4) parallelogram 2 diagonals 2 bisectors of sides isosceles trapezoid 14. ASA Congruence Postulate Parallelogram Diagonal Lemma Opposite Sides Theorem Converse of the IT Theorem Opposite Angles Theorem Converse of the Rhombus Angles Theorem Line Postulate Angle Addition Postulate Double-Edged Straightedge Theorem SSS Congruence Postulate IT Theorem Converse of the Angle Bisector Theorem 15a. A 15b. S 15c. S 15d. N 16. 2386 ft 2 17. See table below. 18. V 1 V 2 has length 12.8 and bearing 72.6°. 19a. B 19b. A 20a. 19° 20b. 52° 20c. 52° 20d. 232° 20e. 19° Name Lines of symmetry Rotational symmetry none 2-fold trapezoid none none kite 1 diagonal none square 4-fold rectangle 2 bisectors of sides 2-fold rhombus 2 diagonals 2-fold 1 bisector of sides none
LESSON 13.5 1. D: Paris is in France; Tucson is in the U.S.; London is in England. Bamako must be the capital of Mali. 2. C: The “Sir” in part A shows that Halley was English; Julius Caesar was an emperor, not a scientist; Madonna is a singer. Galileo Galilei must be the answer. 3. No, the proof is claiming only that if two particular angles are not congruent, then the two particular sides opposite them are not congruent. It still might be the case that a different pair of angles are congruent and that therefore a different pair of sides are congruent. 4. Yes, this statement is the contrapositive of the conjecture proved in Example B, so they are logically equivalent. 5. 1. Assume the opposite of the conclusion; 2. Triangle Sum Theorem; 3. Substitution property of equality; 4. 0°; Subtraction property of equality 6. Assume ZOID is equiangular. Use the definition of equiangular and the Four Congruent Angles Rectangle Theorem to prove that ZOID is a rectangle. Therefore ZOID is a parallelogram, which creates a contradiction. 7. Assume CD is the altitude to AB. Use the definitions of altitude, median, and midpoint, the Right Angles Are Congruent Theorem, and the SAS Congruence Postulate to get ADC BDC. Therefore AC BC, which creates a contradiction. 8. Assume ZO ID. Use the Opposite Sides Parallel and Congruent Theorem to prove that ZOID is a parallelogram, which creates a contradiction. 9. Given: Circle O with chord AB and perpendicular bisector CD Show: CD passes through O Assume CD does not pass through O. Use the Line Postulate to construct OB and OA and the Perpendicular Postulate to construct OE. Then use the Isosceles Triangle Theorem, the Right Angles Are Congruent Theorem, and the SAA Theorem to get OEA OEB. From CPCTC and the definition of midpoint, prove that E is the midpoint of AB, which creates a contradiction. C O 10. a 75°, b 47°, c 58° 11. 42 ft3 132 ft 3 12a. 12b. 1 3 13a. A 13b. N 13c. S 13d. S 13e. A 3 3 4 12 B D E A ANSWERS TO EXERCISES 151 <strong>Answers</strong> to Exercises
Page 1 and 2:
Answers to Exercises 0 CHAPTER 0
Page 3 and 4:
LESSON 0.3 1. Design with reflectio
Page 5 and 6:
LESSON 0.5 1. possible answers: Sco
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CHAPTER 0 REVIEW 1. possible answer
Page 9 and 10:
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
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1 OR CD ? 5 OC OD ? All radii o
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LESSON 6.5 1. d 5 cm 2. C 10 cm 3
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1. 1 2 ,3 USING YOUR ALGEBRA SKILL
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CHAPTER 6 REVIEW 1. Answers will va
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Answers to Exercises CHAPTER 7 •
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15. possible answer: HIKED 16. one,
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LESSON 7.4 1. Answers will vary. 2.
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LESSON 7.6 1. Answers will vary. 2.
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1. parallelograms 2. parallelograms
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CHAPTER 7 REVIEW 1. true 2. true 3.
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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 105 and 106: Answers to Exercises CHAPTER 9 •
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 and 128: LESSON 11.3 1. 16 m 2. 4 ft 3 in. 3
Page 129 and 130: 1. 18 cm 2. 12 cm 3. 21 cm 4. 15 cm
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: 1. A LESSON 13.4 Use x to represent
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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