Similarity in Right Triangles GEOMETRY LESSON 8-4 Pages 435-438 Exercises 9. s 10. r 11. c 12. a; a 13. h 14. b 15. 9 16. 20 1. 6 2. 2 10 3. 4 3 4. 12 5. 14 2 6. 25 7. 6 6 8. 3 7 17. 10 18. 6 3 19. 12 20. 60 21. a. 18 mi b. 24 mi 22. KNL; JNK 8-4

Similarity in Right Triangles GEOMETRY LESSON 8-4 23. a. 4 cm b. c. Answers may vary. Sample: Draw a 10-cm segment. 2 cm from one endpoint, construct a of length 4 cm. Connect to form a . 24. a.  b. They are =. Explanations may vary. Sample: The altitude and hyp. segments are sides of two isosc. . 25. (10, 6), (–2, 6) s 26. 4 3 27. 14 28. 4 29. 14 30. 1 31. 2.5 32. 10 10 33. 121 8-4

Similarity in Right Triangles GEOMETRY LESSON 8-4 34. x = 12; y = 3 7; z = 4 7 35. x = 12 5; y = 12; z = 6 5 36. x = 4; y = 2 13; z = 3 13 37. 12 2 38. a. Given b. Corollary 2 of Thm. 8-3 12 5 9 16 20 3 25 38. (continued) c. Cross-Product Prop. d. Addition Prop. of = e. Dist. Prop. f. Segment Add. Post. g. Subst. 39. about 6.5 m 40. 5 3 cm 60 13 144 41. h = 5, a = , h1 = , h2 = 42. 1 = 2 13, 2 = 3 13, h = 13, a = 6 43. 1 = 2 = 6 2, h = 12, h2 = 6 44. 2 = , h = , h1 = 3, h2 = 45. 1 = 5, a = , h1 = , h2 = 8-4

Similarity in Right Triangles GEOMETRY LESSON 8-4 52. 4.5 53. 54. 55. 56. 57. D 58. G 59. C 60. H 49. a. Given: rt. ABC with alt. CD; Prove: AC • BC = AB • CD b. Yes; AC • BC = 2 X area ABC and AB • CD = 2 X area ABC. 50. 3 51. 4 4 7 3 16 7 12 5 60 13 120 17 420 29 46. 2 = , h = , a = 7, h2 = 47. 1 = 8 5, 2 = 4 5, h1 = 4, h2 = 20 48. 1 = 6, h = 12, a = 3 3, h2 = 9 8-4

Similarity in Right Triangles GEOMETRY LESSON 8-4 68. x = 6; y = 9 69. x = 3; y = 4 61. [2] a. Solve for x by making a proport. from similar rt. . The proportion is = . Now cross multiply and solve for x. b. 3 13 [1] incorrect proportion OR incorrect x value 62. a. RNM ~ PNQ b. AA ~ Post. 63. a. PRQ ~ ACB b. SSS ~ Thm. 64. not similar 65. 7.5 66. 10 67. x = 5; y = 8 s x 13 9 8-4