1. Inequalities in Triangles
GEOMETRY LESSON 5-5
because they are vertical and m 1 > m 3 by Corollary to the Ext. Thm. So, m 1 > m 2 by subst.
2. An ext. of a is larger than either remote int
3. m 1 > m 4 by Corollary to the Ext.
Thm. and
2 because if
Pages Exercises
3. (continued)
lines, then alt. int are .
M, L, K
D, C, E
G, H, I
A, B, C
E, F, D
Z, X, Y
10. MN, ON, MO
11. FH, GF, GH
12. TU, UV, TV
13. AC, AB, CB
14. EF, DE, DF
15. ZY, XZ, XY
16. No;
17. Yes; > 15; > 11; > 12 s
>
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2. Inequalities in Triangles
GEOMETRY LESSON 5-5
< s < 21
24. 0 < s < 12
< s < 41
26. 3 < s < 11
< s < 55
28. Answers may vary. Sample: If Y is the distance between Wichita and Topeka, then 20 < Y < 200.
29. Let the distance between the peaks be d and the distances from the hiker to each of the peaks be a and b. Then d + a > b and
d + b > a. Thus,
d > b – a and
d > a –b.
18. No;
19. Yes; > 15;
> 11.
20. Yes; > 10;
> 2;
> 9.
21. No;
22. 4 < s < 20
>
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3. Inequalities in Triangles
GEOMETRY LESSON 5-5
30. a.
b. the third side of the 1st is longer than the third side of the 2nd .
c. See diagram in part (a).
d. The included of the first is greater than the included of the second .
31. Answers may vary. Sample: The shortcut across the grass is shorter than the sum of the two paths.
32. AB
33. a. m OTY
b. m 3
c. Base of an isosc. are .
d Add. Post.
e. Comparison Prop. of Ineq.
f. Subst. (step 2)
g. An ext. of a is greater than either remote int. s .
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4. Inequalities in Triangles
GEOMETRY LESSON 5-5
33. (continued)
h. Trans. Prop. of Ineq.
34. RS
35. CD
36. XY
37.
38. (2, 4), (2, 5), (2, 6),
(3, 3), (3, 4), (3, 6),
(3, 7), (4, 3), (4, 4),
(4, 5), (4, 6), (4, 7),
(4, 8) 1 2
39.
40.
CD = AC was given so ACD is isosc. By def. of isos This means m D = m CAD. Then
m DAB > m CAD by the Comparison Prop. of Ineq. So by subst., m DAB > m D and by Thm DB > AB. Since DC + CB = DB, by subst. DC + CB > AB. Using subst. again, AC + CB > AB.
T is the largest in PTA. Thus PA > PT because the longest side of a is opp. The largest . 5 18
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5. Inequalities in Triangles
GEOMETRY LESSON 5-5
42. D
43. A
44. B
45. C
46. B
47. [2] a. Since m A > m C > m B, the sides
opp. them are related in the same way:
BC > AB > AC. Of AB and AC, AB is longer than AC. Since 9 in. > 5 in., AB = 9 in. and AC = 5 in.
b. BC is the longest side, so 9 < BC < 14. The possible whole number measures for BC are 10 in., 11 in., 12 in., and 13 in.
[1] part (a) OR part (b) incorrect
48. m A > m B
49. m X ≤ m B
50. The angle is not a right angle.
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6. Inequalities in Triangles
GEOMETRY LESSON 5-5
51. The triangle is obtuse.
52. 90
53. 35
55. 55
ft2
mm2 m2
mi2
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