1. Proportions in Triangles
GEOMETRY LESSON 8-5
Pages Exercises
1. 7.5
2. 8
3. 5.2
4. d
5. c
6. b
7. d
8. 7.5
9. 3
11. 6
13. 35
15.
16. 12 1 3 40 7
17. KS
18. SQ
19. JP
20. KP
21. KM
22. PM
23. JP
24. LW
8-5

2. Proportions in Triangles
GEOMETRY LESSON 8-5 ft ft
cm and 9.2 cm
28. Answers may vary. Sample: 9 cm and 13.5 cm
29. x = 18 m; y = 12 m
30. a.
b. isosceles; Bisector Thm.
31. 20
33. 9
34. a. b.
c. =
35. Measure AC, CE, and BD. Use the Side-Splitter Thm. Write the
proport = and solve for AB.
cm or 12.5 cm
37. 6
40. h = 10.0, h1 = 4.3, h2 = 5.7
41. h = 13.0, 1 = 5.3, 2 = 11.9
= 5.0, h1 = 3.8, h2 = 9.2 AB BC WX XY AC CE BD
8-5

3. Proportions in Triangles
GEOMETRY LESSON 8-5
Given
2. Prop. of Proportions
3. Segment Add. Post.
4. Reflexive Prop. of
5. SAS ~ Thm.
6. Corr. of ~ are .
7. If corr. are , lines are ||.
48. Yes; since = , the segments are || by the Converse of the Side-Splitter Thm.
49. No;
50. Yes; since = , the segments are || by the Converse of the Side-Splitter Thm. x y s 6 10 9 15 28 12 24 20 16
= 7.1, h2 = 5.0, h = 10.0
44. h = 17.0, h1 = 11.1, h2 = 5.9
45. h2 = 4, 1 = 5.7, 2 = 5.7
46. The ratio of the legs of a 30°-60°-90° is
3. Let the rt. bisector divide the hyp. into segments x and y. Then by the
Bis. Thm.,
= 3, so x = 3 y. = /
8-5

4. Proportions in Triangles
GEOMETRY LESSON 8-5
51. (continued)
1.  ABCD (Given)
2.  AE || BF and ED || FC (Def. of )
3. AD BC (Opp. sides of are .)
4. E and F are midpts. of AD and BC. (Given)
5. AE = ED = AD; BF = FC = BC (Def. of midpt.)
6. AE = BF, ED = FC (Subst.)
7. ABFE and EFCD are (If one pair of opp. sides of a quad. is and ||, it is a .)
8. AB || EF and EF || CD (Opp. sides of a are ||.)
51. a. A midsegment of a connects the midpts. of 2 opp. sides.
Given: ABCD with EF connecting the midpts. of AD and BC Prove: AB || EF; EF || CD 1 2 s b.
8-5

5. Proportions in Triangles
GEOMETRY LESSON 8-5
51. (continued) c.
Given: ABCD with midsegment EF Prove: EF bisects AC and BD.
Since AB || EF || DC by part (b), and EF bisects AD, by the Side-Splitter Thm., EF bisects AC and BD.
52. D
53. F
54. [2]  = ; 35n + 35 = 560; n = 15
[1] correct proportion solved incorrectly
55. [4] a.
b.  =
x = 4.8 cm =
y = 7.5 cm
n + 1 28 20 35 x 4 6 5 6 4 y 5
8-5

6. Proportions in Triangles
GEOMETRY LESSON 8-5
65. RT = SV = 48
66. RT = SV = 6.5
55. (continued)
[3] correct drawings and proportions with one computational error
[2] one possibility drawn and done correctly OR two correct drawings
[1] one correct drawing OR one correct proportion
56. m
57. m
58. c
59. h
60. x = 24; y =
61. x = 9; y =
62. x = 15; y = 30
63. RT = SV = 38
64. RT = SV = 37
8-5