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<strong>Answers</strong> to Exercises USING YOUR ALGEBRA SKILLS 3 1. perpendicular 2. neither 3. perpendicular 4. parallel 5. possible answer: (2, 5) and (7, 11) 6. possible answer: (1, 5) and (2, 12) 7. Ordinary; no two slopes are the same, so no sides are parallel, although TE EM because their slopes are opposite reciprocals. 8. Ordinary, for the same reason as in Exercise 7— none of the sides are quite parallel. 9. trapezoid: KC RO 10a. Slope HA slope ND 1 6 ; slope HD slope NA 6. Quadrilateral HAND is a rectangle because opposite sides are parallel and adjacent sides are perpendicular. 40 ANSWERS TO EXERCISES 10b. Midpoint HN midpoint AD 1 diagonals of a rectangle bisect each other. 11a. Yes, the diagonals are perpendicular. Slope OE 1; slope VR 1. 11b. Midpoint VR midpoint OE (2, 4). The diagonals of OVER bisect each other. 11c. OVER appears to be a rhombus. Slope 2 ,3.The OV slope RE 1 5 and slope OR slope VE 5, so opposite sides are parallel. Also, all of the sides appear to have the same length. 12a. Both slopes equal 1 2 . 12b. The segments are not parallel because they are coincident. 12c. distinct 13. (3, 6)
LESSON 3.6 1. Sample description: Construct one of the segments, and mark arcs of the correct length from the endpoints. Draw sides to where those arcs meet. M A M 2. O Sample description: Construct O. Mark off distances OD and OT on the sides of the angle. Connect D and T. 3. I I D O M A O D O Y I Y A Y S T T Sample description: Construct IY. Construct I at I and Y at Y. Label the intersection of the rays point G. 4. Yes, students’ constructions must be either larger or smaller than the triangle in the book. Sample description: Draw one side with a different length than the lengths in the book. Duplicate an S S G angle at each end of that segment congruent to one of the angles in the book. Where they meet is the third vertex of the triangle. 5. A A C Sample description: Construct A and mark off the distance AB. From B swing an arc of length BC to intersect the other side of A at two points. Each gives a different triangle. 6. C y x ____ 2 A y x C T B B y x ____ 2 x Sample description: Mark the distance y, mark back the distance x, and bisect the remaining length of y x. Using an arc of that length, mark arcs on the ends of segment x. The point where they intersect is the vertex angle of the triangle. 7. Sample description: Draw an angle. Mark off equal segments on the sides of the angle. Use a different compass setting to draw intersecting arcs from the ends of those segments. 8. Sample description: Draw an angle and mark off unequal distances on the sides. At the endpoint of the longer segment (not the angle vertex), swing an arc with the length of the shorter segment. From the endpoint of the shorter segment, swing an arc the length of the longer segment. Connect the endpoints of the segments to the intersection points of the arcs to form a quadrilateral. ANSWERS TO EXERCISES 41 <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
Page 7 and 8: CHAPTER 0 REVIEW 1. possible answer
Page 9 and 10: USING YOUR ALGEBRA SKILLS 1 1. (3,
Page 11 and 12: 34. B 35. MY; CK; mI 36. SEU; EUO;
Page 13 and 14: 20. false 21. true 22. false; Thoug
Page 15 and 16: LESSON 1.5 1. D 2. A 3. C 4. B 5. C
Page 17 and 18: LESSON 1.7 1. Answers will vary. Sa
Page 19 and 20: LESSON 1.8 1. 2. 3. 4. 5. 6. 7. 8.
Page 21 and 22: CHAPTER 1 REVIEW 1. true 2. False;
Page 23 and 24: Answers to Exercises CHAPTER 2 •
Page 25 and 26: 8. 8n is steeper; the coefficient o
Page 27 and 28: LESSON 2.4 1. inductive; deductive
Page 29 and 30: LESSON 2.6 1. 63° 2. 90° 3. no 4.
Page 31 and 32: CHAPTER 2 REVIEW 1. poor inductive
Page 33 and 34: 1. 2. 3. 4. 5. A B Q D C D 1 CD 2 E
Page 35 and 36: 1. LESSON 3.3 The answer depends on
Page 37 and 38: 1. D 2. F 3. A 4. C 5. E 6. 7. 8. 9
Page 39: LESSON 3.5 1. 2. 3. Construct a seg
Page 43 and 44: 1. incenter LESSON 3.7 Because the
Page 45 and 46: LESSON 3.8 1. The center of gravity
Page 47 and 48: 42. true 43. False; any non-acute t
Page 49 and 50: LESSON 4.2 1. 79° 2. 54° 3. 107.5
Page 51 and 52: 1. yes 2. no 3. no 4 5 9 5 6 12 LES
Page 53 and 54: LESSON 4.5 1. If two angles and the
Page 55 and 56: 1. See flowchart below. 2. See flow
Page 57 and 58: 1. 6 2. 90°; 18° 3. 45° 4. See f
Page 59 and 60: CHAPTER 4 REVIEW 1. Their rigidity
Page 61 and 62: Answers to Exercises 5 CHAPTER 5
Page 63 and 64: LESSON 5.3 1. 64 cm 2. 21°; 146°
Page 65 and 66: 1. 34 cm; 27 cm 2. 132°; 48° 3. 1
Page 67 and 68: 1. 2. 3. (0, 4) y y y (0, 6) USING
Page 69 and 70: 22. The platform stays parallel to
Page 71 and 72: 7. 2 RE AB 3 BR EA 4 AR EB
Page 73 and 74: 20. Speed: 901.4 km/h. Direction:
Page 75 and 76: 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 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
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1. 18 cm 2. 12 cm 3. 21 cm 4. 15 cm
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1. 1715 cm 3 LESSON 11.6 2. 16 cm,
Page 133 and 134:
Use segment addition to show that e
Page 135 and 136:
Page 137 and 138:
LESSON 12.3 1. 329 cm 2 2. 4 cm 2 3
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LESSON 12.5 1. approximately 12.7 m
Page 141 and 142:
13. f(x) 1 2 (x3)2 2; A vertical s
Page 143 and 144:
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
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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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