1. a. Add. Post. b. Subst. Prop. c. Simplify.

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1. a. Add. Post. b. Subst. Prop. c. Simplify. Reasoning in Algebra GEOMETRY LESSON 2-4 Pages 91-94 Exercises 1. a. Add. Post. b. Subst. Prop. c. Simplify. d. Subtr. Prop. of = e. Div. Prop. of = 2. a. Segment Add. Post. b. Subst. Prop. c. Distributive Prop. d. Simplify e. Subtr. Prop. of = f. Div. Prop. of = 3. a. Mult. Prop. of = b. Distr. Prop. c. Add. Prop. of = 4. a. Distr. Prop. b. Subtr. Prop. of = c. Div. Prop. of = 5. Reflexive Prop. of 6. Distr. Prop. 7. Div. Prop. of = 8. Symmetric Prop. of 9. Mult. Prop. of = 10. Reflexive Prop. of = 11. Subtr. Prop. of = 12. Symmetric Prop. of = 13. Sub. Prop. 14. Add. Prop. of = 15. Transitive Prop. of = 16. 15 17. 5x 2-4

28. a. 1. KL + LM = KM (Segment Add. Post.) Reasoning in Algebra GEOMETRY LESSON 2-4 18. YU = AB 19. K 20. PQR 21. 3 22. EF + 7 23. XYZ WYT 24. TR = 3UW 25. Answers may vary. Sample: LR and RL are different ways to name the same segment and CBA and ABC are different ways to name the same . 26. C 27. a. Given b. Def. of midpoint c. Subst. Prop. of = d. Subtr. Prop. of = e. Div. Prop. of = 28. a. 1. KL + LM = KM (Segment Add. Post.) 2. 2x – 5 + 2x = 35 (Subst. Prop.) 3. 4x – 5 = 35 (Simplify.) 4. 4x = 40 (Add. Prop. of =) 5. x = 10 (Div. Prop. of =) b. 15 2-4

29. a. 1. m GFE + m EFI = m GFI ( Addition Post.) Reasoning in Algebra GEOMETRY LESSON 2-4 29. a. 1. m GFE + m EFI = m GFI ( Addition Post.) 2. 9x – 2 + 4x = 128 (Subst. Prop.) 3. 13x – 2 = 128 (Simplify.) 4. 13x = 130 (Add. Prop. of =) 5. x = 10 (Div. Prop. of =) b. 40 30. a. Given b. Def. of Bisector c. Subst. Prop. d. Subtr. Prop. Of = e. Div. Prop. Of = 31. In the fifth step, each side is divided by (b – a). But b – a = 0 and division by 0 is not defined. 32. reflexive, symmetric, transitive 33. transitive 34. reflexive, symmetric, transitive 35. symmetric 36. reflexive, symmetric, transitive 37. transitive 38. D 39. B 40. D 2-4

b. 3y = 105 Subtr. Prop. of Equality y = 35 Div. Prop. of Equality Reasoning in Algebra GEOMETRY LESSON 2-4 41. A 42. [2] a. 2y + 15 + y = 120 Subst. Prop. 3y + 15 = 120 Simplify. b. 3y = 105 Subtr. Prop. of Equality y = 35 Div. Prop. of Equality x = 2y + 15 x = 2(35) + 15 x = 85 [1] solved for y only, OR no work shown 43. Elena’s teacher is concerned. 44. If a person has a job, then that person can save money each week. 45. 80 46. 125 47. 65 48. 90 49. Answers may vary. Sample: AOD, BOE 50. 29, 31.5 51. 3.45678, 3.456789 52. –162, 486 53. , – 1 2 4 2-4