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<strong>Answers</strong> to Exercises 1. T B H A LESSON 13.7 Use the Right Angles Are Congruent Theorem, CASTC, and the AA Similarity Postulate to get BT TH BHT GEV. Therefore, GV VE by CSSTP. See the Solutions Manual for the family tree. 2. A G S L M Use the definitions of median and midpoint, the Segment Addition Postulate, the substitution property, and the multiplication property to get BY 1 BI 2 and SL 1 SM. 2 Then use CASTC, CSSTP, and the SAS Similarity Theorem to get BYG SLA. Therefore, BG GY SA AL by CSSTP. See the Solutions Manual for the family tree. 3. C F 1 3 A B P Use the definition of angle bisector, the Angle Addition Postulate, and the substitution property to get mACB 2m1 and mDFE 2m2. Then use CASTC and the AA Similarity Postulate to get APC DQF. Therefore, AC CP DF FQ by CSSTP. 4. C D E 1 2 A B Use the CA Postulate and the AA Similarity Postulate to get CDE CAB. Then use CSSTP and the Segment Addition Postulate to get CD DA CD CE EB DA EB . CE Therefore, CD CE by algebra. 5. C D E 1 2 A B 2 4 D E Q DA EB Use the addition property to get CD 1 CE 1. Then use algebra and the Segment Addition CA CB Postulate to get CD . CE Therefore ABC DEC by the SAS Similarity Theorem, 1 2 by CASTC, and DE AB by the CA Postulate. 154 ANSWERS TO EXERCISES G V E B Y I L 6. Use the Right Angles Are Congruent Theorem, the reflexive property, and the AA Similarity Postulate to get ADC ACB and ACB CDB. Therefore, ADC ACB CDB by the transitive property of similarity. 7. C Use the Three Similar Right Triangles Theorem to get ADC CDB. Then use CSSTP to get x h h y . 8. A A Draw the altitude to the hypotenuse, then use the ratios given by the Three Similar Right Triangles a c yields a2 c2 cd. Theorem. In particular, c d a b c Now look at the other small triangle and use d b to get b2 cd. 9. C Begin by constructing a second triangle, right triangle DEF (with E a right angle), with legs of lengths a and b and hypotenuse of length x. The plan is to show that x c, so that the triangles are congruent. Then show that C and E are congruent. Once you show that C is a right angle, then ABC is a right triangle. 10. H L Y a d C 1 2 D h x D y b a c B A c b c – d P E B B D F x Use the Pythagorean Theorem to write expressions for the lengths of the unknown legs. Show that the expressions are equivalent. The triangles are congruent by SSS or SAS. a E G b
11. CA Postulate 12. 13. Perpendicular Postulate Segment Duplication Postulate Parallel Postulate CA Postulate AA Similarity Postulate SAS Congruence Postulate SAS Similarity Theorem SSS Similarity Theorem Three Similar Right Triangles Theorem Pythagorean Theorem Segment Addition Postulate Parallel/Proportionality Theorem AA Similarity Postulate Right Angles Are Congruent Theorem SSS Congruence Postulate AA Similarity Postulate 14. approximately 1.5 cm or 6.5 cm 15a. C 15b. A 15c. A 15d. A 15e. C 16a. The vectors are diagonals of your quadrilateral. 16b. A 180° rotation about the midpoint of the common side; the entire tessellation maps onto itself. 17a. a 180° rotation about the midpoint of any side 17b. possible answer: a vector running from each vertex of the quadrilateral to the opposite vertex (or any multiple of that vector) 18a. 33° 18b. 66° 18c. 57° 18d. 62° 18e. PSQ and PTQ are 90° by the Tangent Theorem and so are supplementary. So, SPT and SQT must also be supplementary by the Quadrilateral Sum Theorem. Therefore, opposite angles are supplementary, so it’s cyclic. 18f. Because PS is a tangent, mPSQ 90° (Tangent Theorem). Because mPSQ 90°, SQ must be a tangent (Converse of the Tangent Theorem). 19a. 12 1 19b. 3 2 3 6 4 1 20a. CDG CFG by SAA; GEA GEB by SAS; DGA FGB by the HL Theorem 20b. CD CF and DA FB by CPCTC; CD DA CF FB (addition property of equality). Therefore, CA CB, and ABC is isosceles. 20c. The figure is inaccurate. 20d. The angle bisector does not intersect the perpendicular bisector inside the triangle as shown, except in the special case of an isosceles triangle, when they coincide. 21. 173 cm, 346 cm, 20 stones. Draw the trapezoid and extend the legs until they meet to form a triangle. Use parallel proportionality to find the rise. The span is twice the rise. Use inverse tangent to find the central angle measure. Divide into 180° to find the number of voussoirs. ANSWERS TO EXERCISES 155 <strong>Answers</strong> 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
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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
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USING YOUR ALGEBRA SKILLS 8 1. x 2
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LESSON 8.5 1. 9 in 2 2. 49 cm 2 3.
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Page 107 and 108: USING YOUR ALGEBRA SKILLS 9 1. 6 2.
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Page 117 and 118: LESSON 10.3 1. 192 cm3 2. 84 cm3 2
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Page 121 and 122: LESSON 10.7 1. V 972 cm3 3054 cm3
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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
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Page 151 and 152: LESSON 13.5 1. D: Paris is in Franc
Page 153: 8. Use the Inscribed Angle Theorem
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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