Pythagorean Theorem and its Converse

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Pythagorean Theorem and its Converse GEOMETRY LESSON 7-2 Pages 360-364 Exercises 1. 10 2. 7 3. 34 4. 12 5. 65 6. 8 7. No; 42 + 52 62. 8. Yes; 102 + 242 = 262. 9. Yes; 152 + 202 = 252. 10. 41 11. 33 12. 3 11 13. 2 89 14. 3 2 15. 5 2 16. 14 ft 9 3 2 = / 17. 17.0 m 18. m2 19. 12 7 cm2 20. 25 3 in.2 21. No; 192 + 202 282. 22. No; 82 + 242 252. 23. Yes; 332 + 562 = 652. 24. obtuse 7-2

Pythagorean Theorem and its Converse GEOMETRY LESSON 7-2 25. right 26. acute 27. right 28. obtuse 29. acute 30. obtuse 31. right 32. acute 33. obtuse 34. right 35. acute 36. 10 37. 8 5 38. 2 2 39. Answers may vary. Sample: Have three people hold the rope 3 units, 4 units, and 5 units apart in the shape of a triangle. 40. 10.5 in.2 41. 168 ft2 42. 14 m2 43. 32 in.2 44. 4.2 in. 45. Yes; 72 + 242 = 252, so RST is a rt. . 7-2

Pythagorean Theorem and its Converse GEOMETRY LESSON 7-2 46. a. |x2 – x1|; |y2 – y1| b. PQ2 = (x2 – x1)2 + (y2 – y1)2 c. PQ = (x2 – x1)2 + (y2 – y1)2 47. Answers may vary. Sample: Using 2 segments of length 1, construct the hyp. of the right formed by these segments. Using the hyp. found as one leg and a segment of length 1 as the other leg, construct the hyp. of the formed by those legs. Continue this process until constructing a hypotenuse of length n. 48. 29 49. 50 50. 84 51. 35 52–59. Answers may vary. Samples are given. 52. 6; 7 53. 4; 5 54. 8; 11 7-2

Pythagorean Theorem and its Converse GEOMETRY LESSON 7-2 55. 11; 12 56. 8; 10 57. 14; 16 58. 18; 19 59. 39; 42 60. a. c2 b. 2ab + (b – a)2 c. c2 = a2 + b2 61. 2830 km BD2 + AC2 + BC2 62. 12 cm 63. 12.5 cm 64. 17.9 cm 65. a. Answers may vary. Sample: n = 6; 12, 35, 37 b. 122 + 352 = 372 66. a. 5 in. b. 29 c. d2 = d. 34 in. 7-2

Pythagorean Theorem and its Converse GEOMETRY LESSON 7-2 67. 14 68. 61 69. 17 70. Draw right FDE with legs DE of length a and EF of length b and hyp. of length x. Then a2 + b2 = x2 by the Pythagorean Thm. We are given ABC with sides of length a, b, c and a2 + b2 = c2. By subst., c2 = x2, so c = x. Since all side lengths of ABC and FDE are the same, ABC FDE by SSS. C E by CPCTC, so m C = 90. Therefore, ABC is a right . 71. 26.2 72. 30 73. 9 74. 37 75. 14.1 76. 72 cm2 77. 15 ft 78. 7; 33 79. 3; 20 80. 10 81. 3 82. 50 83. 7 7-2