1. Parallel Lines and the Triangle Angle-Sum Theorem
GEOMETRY LESSON 3-3
Pages Exercises
1. 30
3. 90
4. 71
5. 90
6. x = 70; y = 110; z = 30
7. t = 60; w = 60
8. x = 80; y = 80
9. 70
10. 30
11. 60
12. acute, isosceles
13. acute, equiangular, equilateral
14. right, scalene
15. obtuse, isosceles
16.
17. Not possible; a right will always have one longest side opp. the right .
18.
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2. Parallel Lines and the Triangle Angle-Sum Theorem
GEOMETRY LESSON 3-3
19.
20.
21.
22.
23.
24. a. 5, 6, 8
b and 3 for 5
1 and 2 for 6
1 and 2 for 8
c. They are vert. .
25. a. 2
b. 6 s
28. m 3 = 92; m 4 = 88
29. x = 147, y = 33
30. a = 162, b = 18
31. x = 52.5; 52.5, 52.5, 75; acute
32. x = 7; 55, 35, 90; right
33. x = 37; 37, 65, 78; acute
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3. Parallel Lines and the Triangle Angle-Sum Theorem
GEOMETRY LESSON 3-3
34. x = 38, y = 36, z = 90;
ABD: 36, 90, 54; right; BCD: 90, 52, 38; right; ABC: 74, 52, 54; acute
35. a = 67, b = 58, c = 125, d = 23, e = 90; FGH: 58, 67, 55; acute;
FEH: 125, 32, 23; obtuse; EFG: 67, 23, 90; right
36. x = 32, y = 62, z = 32, w = 118; ILK: 118, 32, 30; obtuse
37. 60; 180  3 = 60
38. Yes, an equilateral is isosc. Because if three sides of a are , then at least two sides are . No, the third side of an isosc. does not need to be to the other two.
39. eight
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4. Parallel Lines and the Triangle Angle-Sum Theorem
GEOMETRY LESSON 3-3
41. Check students’ work. Answers may vary. Sample: The two ext.
Formed at vertex A are vert. and thus have the same measure.
and 60
43. a. 40, 60, 80
b. acute s
47. 32
48. a. 90
b. 180
c. 90
d. compl.
e. compl.
49. a. Add.
b Sum
c. Trans.
d. Subtr. s
; since the missing
is 68, the largest ext. Is 180 – 48 = 132.
51. Check students’ work.
52. a. 81
b. 45, 63, 72
c. acute
or 60
or 45
55. 90
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5. Parallel Lines and the Triangle Angle-Sum Theorem
GEOMETRY LESSON 3-3
56. Greater than, because there are two with measure 90 where the meridians the equator.
57.
58.
59. 1
60.
61. 0 s 1 3 7 19
63. Answers may vary. Sample: The measure of the ext. is = to the sum of the measures of the two remote int Since these are , the formed by the bisector of the ext. are to each of them. Therefore, the bisector is || to the included side of the remote int. by the Conv. of the Alt Int. Thm.
64. B
65. G
66. B
67. H s
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6. Parallel Lines and the Triangle Angle-Sum Theorem
GEOMETRY LESSON 3-3
68. [2] a.
b. The correct equation is 2x = (2x – 40) + (x – 15) with the sol. x = 55. The three int measure 70, 40, and 70.
[1] incorrect sketch, equation, OR solution
69. [2] a. 159; the sum of the three of the is 180, so m Y + m M + m F = 180. Since m F = 21, m Y + m M + 21 = 180. Subtr. 21 from both sides results in m Y + m M = 159.
69. (continued)
b. 1 to 68 ; since Y is obtuse, its whole number range is from 91 to 158, allowing the measure of 1 for m M when m Y = When m Y = 91, then m M = 68.
[1] incorrect answer to part (a) or (b) OR incorrect computation in either part s s
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7. Parallel Lines and the Triangle Angle-Sum Theorem
GEOMETRY LESSON 3-3
70. 53
71. 46
72. 7
73.
74.
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