Proving Angles Congruent GEOMETRY LESSON 2-5 Pages 100-103 Exercises 1. AOB or DOC 2. EOC 3. EOC 4. DOC or AOB 5. AOB and DOC or BOC and AOD 6. 90 7. 30 8. 150 9. 30 10. Yes; the markings show they are . 11. No; there are no markings. 12. Yes; you can conclude that are adjacent and suppl. from the diagram. 13. No; there are no markings. s 14. Yes; you can conclude that are suppl. from the diagram. 15. Yes; there are markings. 16. No; there are no markings. 17. Yes; you can conclude that are vert. from the diagram. 18. No; there are no markings. s s 2-5

Proving Angles Congruent GEOMETRY LESSON 2-5 19. a. 90 b. 90 c. Subst. d. m 3 20. 20 21. x = 25, y = 105 22. 30 23. 60, 60 24. 75, 105 25. 120, 120 26. Answers may vary. Sample: A thm. is proven and a post. is assumed to be true. 27. Answers may vary. Sample: scissors 28. If m 1 + m 2 = 180, and m 2 + m 3 = 180, then m 1 + m 2 = m 2 + m 3 by subst. Subtr. m 2 from each side m 1 = m 3 or 1 3. 29. 15; 25, 25 30. x = 14, y= 15; 50, 50, 130 31. a. rt. b. m Y 32. DOB AOC and DOA BOC since they are vert. . 33. EIG FIH since all rt. are ; EIF HIG since they are compl. of the same . s 2-5

Proving Angles Congruent GEOMETRY LESSON 2-5 34. KPJ MPJ since they are marked ; KPL MPL since they are suppl. of . 35. a. V b. 180 c. Division d. right 36. The two acute have measure 72. The two obtuse have measure 108. s 37. a. Answers may vary. B can be any point on the positive y-axis. Sample: (0, 5) b. Answers may vary. Sample: (3, –1) 38. Answers may vary. Sample: (–5, –1) 39. 9; 36 40. 10; 105, 75 41. 18; 54, 36 42. 11; 49, 41 43. Suppl. of are . 44. 90, 90 45. 45, 45 46. Not possible; a pair of vertical can have any measure greater than 0 or less than 180. 47. m A = 72, m B = 18 s 2-5

Proving Angles Congruent GEOMETRY LESSON 2-5 48. m A = 126, m B = 54 49. m A = 60, m B = 30 50. m A = 30, m B = 60 51. m A = 120, m B = 60 52. m A = 90, m B = 90 53. m A = 60, m B = 120, m C = 30 54. m A = 72, m B = 18, m C = 108 55. By the def. of suppl. , m 1 + m 2 = 180 and m 3 + m 4 = 180. By the Subst. Prop. m 1 + m 2 = m 3 + m 4. It is given that 2 4, so m 2 = m 4. Then by the Subtr. Prop. of =, m 1 = m 3, or 1 3. s 56. By the def. of compl. , m 1 + m 2 = 90 and m 3 + m 4 = 90. By the Subst. Prop. of =, m 1 + m 2 = m 3 + m 4. It is given that 2 4, so m 2 = m 4. Then by the Subtr. Prop. of =, m 1 = m 3 or 1 3. 57. x = 30, y = 90; 60, 120, 60 58. x = 35, y = 70; 70, 110, 70 s 2-5

Proving Angles Congruent GEOMETRY LESSON 2-5 59. x = 50, y = 20; 80, 100, 80 60. 41 61. 45 62. 135 63. 20 64. 90 65. 70 66. 110 67. 12 68. AB 69. 3 + NP = 15 70. not possible 71. 1 and 2 are . 72. If y = 25, then y + 7 = 30 if and only if y = 25 73. If you live south of the equator, then you live in Australia. 74. If n2 > 0, then n > 0. 2-5