1. 1. a. Add. Post. b. Subst. Prop. c. Simplify.
Reasoning in Algebra
GEOMETRY LESSON 2-4
Pages 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
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2. 28. a. 1. KL + LM = KM (Segment Add. Post.)
Reasoning in Algebra
GEOMETRY LESSON 2-4
18. YU = AB K
PQR
21. 3
22. EF + 7
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 = (Subst. Prop.)
3. 4x – 5 = (Simplify.)
4. 4x = (Add. Prop. of =)
5. x = (Div. Prop. of =)
b. 15
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3. 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 = (Subst. Prop.)
3. 13x – 2 = (Simplify.)
4. 13x = (Add. Prop. of =)
5. x = (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
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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 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
47. 65
48. 90
49. Answers may vary. Sample: AOD, BOE
50. 29, 31.5 ,
52. –162, 486
, – 1 2 4
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