1. Proving Angles Congruent
GEOMETRY LESSON 2-5
Pages Exercises
1. AOB or DOC
2. EOC
3. EOC
4. DOC or AOB
5. AOB and DOC or
BOC and AOD
6. 90
7. 30
8. 150
9. 30
10. Yes; the markings show they are .
11. No; there are no markings.
12. Yes; you can conclude that are adjacent and suppl. from the diagram.
13. No; there are no markings. s
14. Yes; you can conclude that are suppl. from the diagram.
15. Yes; there are markings.
16. No; there are no markings.
17. Yes; you can conclude that are vert. from the diagram.
18. No; there are no markings. s s
2-5

2. Proving Angles Congruent
GEOMETRY LESSON 2-5
19. a. 90
b. 90
c. Subst.
d. m 3
20. 20
21. x = 25, y = 105
22. 30
23. 60, 60
24. 75, 105
, 120
26. Answers may vary. Sample: A thm. is proven and a post. is assumed to be true.
27. Answers may vary. Sample: scissors
28. If m m 2 = 180, and m m 3 = 180, then m m 2 = m m 3 by subst. Subtr. m 2 from each side m 1 = m 3 or
29. 15; 25, 25
30. x = 14, y= 15; 50, 50, 130
31. a. rt.
b. m Y
DOB AOC and
DOA BOC since they are vert. .
EIG FIH since all rt. are ; EIF
HIG since they are compl. of the same . s
2-5

3. Proving Angles Congruent
GEOMETRY LESSON 2-5
KPJ MPJ since they are marked ;
KPL MPL since they are suppl. of
35. a. V
b. 180
c. Division
d. right
36. The two acute have measure 72. The two obtuse have measure 108. s
37. a. Answers may vary. B can be any point on the positive y-axis. Sample: (0, 5)
b. Answers may vary. Sample: (3, –1)
38. Answers may vary. Sample: (–5, –1)
39. 9; 36
40. 10; 105, 75
41. 18; 54, 36
42. 11; 49, 41
43. Suppl. of are .
44. 90, 90
45. 45, 45
46. Not possible; a pair of vertical can have any measure greater than 0 or less than 180.
47. m A = 72, m B = 18 s
2-5

4. Proving Angles Congruent
GEOMETRY LESSON 2-5
48. m A = 126, m B = 54
49. m A = 60, m B = 30
50. m A = 30, m B = 60
51. m A = 120, m B = 60
52. m A = 90, m B = 90
53. m A = 60, m B = 120, m C = 30
54. m A = 72, m B = 18, m C = 108
55. By the def. of suppl. , m m 2 = 180 and m m 4 = 180. By the Subst. Prop. m m 2 = m m 4. It is given that , so m 2 = m 4. Then by the Subtr. Prop. of =, m 1 = m 3, or s
56. By the def. of compl. , m m 2 = 90 and m m 4 = 90. By the Subst. Prop. of =, m m 2 = m m 4. It is given that 2
4, so m 2 = m 4. Then by the Subtr. Prop. of =, m 1 = m 3 or
57. x = 30, y = 90; 60, 120, 60
58. x = 35, y = 70; 70, 110, 70 s
2-5

5. Proving Angles Congruent
GEOMETRY LESSON 2-5
59. x = 50, y = 20; 80, 100, 80
60. 41
61. 45
63. 20
64. 90
65. 70
67. 12
68. AB
NP = 15
70. not possible
and 2 are .
72. If y = 25, then y + 7 = 30 if and only if y = 25
73. If you live south of the equator, then you live in Australia.
74. If n2 > 0, then n > 0.
2-5