1. Properties of Parallelograms
GEOMETRY LESSON 6-2
Pages Exercises
1. 127
2. 67
3. 76
4. 124
5. 100
6. 118 7.
8. 4
9. 4
10. 3; 10, 20, 20
11. 22; 18.5, 23.6, 23.6
12. 20
13. 18
14. 17
15. 12;
m Q = m S = 36, m P = m R = 144
16. 6;
m H = m J = 30,
m I = m K = 150
17. x = 6, y = 8
18. x = 5, y = 7
19. x = 7, y = 10
20. x = 6, y = 9
21. x = 3, y = 4
22. 12; 24 3 4
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2. Properties of Parallelograms
GEOMETRY LESSON 6-2
23. Pick 4 equally spaced lines on the paper. Place the paper so that the first button is on the first line and the last button is on the fourth line. Draw a line between the first and last buttons. The remaining buttons should be placed where the drawn line crosses the 2 lines on the paper.
24. 3
25. 3
26. 6
27. 6
28. 9
34. BC = AD = 14.5 in.;
AB = CD = 9.5 in.
35. BC = AD = 33 cm;
AB = CD = 13 cm
36. a. DC
b. AD c.
d. Reflexive
e. ASA
f. CPCTC
6-2

3. Properties of Parallelograms
GEOMETRY LESSON 6-2
37. a. Given
b. Def. of
c. If 2 lines are , then alt. int. are
d. If 2 lines are , then alt. int. are
e. Reflexive Prop. of
37. (continued)
f. ASA h. CPCTC
g. ASA i. CPCTC
38. s
6-2

4. Properties of Parallelograms
GEOMETRY LESSON 6-2
39. 38, 32, 110
40. 81, 28, 71
41. 95, 37, 37
42. The lines going across may not be
since they are not marked as .
43. 18, 162
44. 60
45. x = 15, y = 45
46. x = 109, y = 88,
z = 76
47. x = 25, y = 115
48. x = y = 6
49. x = 10, y = 4
50. x = 12, y = 4
51. x = 0, y = 5
52. x = 9, y = 6
53. The opp. are , so they have =
53. (continued)
measures. Consecutive are suppl., so their sum is 180.
54. a. Answers may vary. Check students’ work.
b. No; the corr. sides can be but the may not be.
55. a. Given
b. Def of a s s s
6-2

5. Properties of Parallelograms
GEOMETRY LESSON 6-2
56. Answers may vary. Sample:
1. LENS and NGTH are s.
(Given)
ELS ENS and GTH GNH
(Opp of a are .)
ENS GNH
(Vertical are .)
ELS GTH
(Trans. Prop. of )
57. Answers may vary. Sample: In LENS and NGTH, GT EH and EH LS by the def. of a
Therefore LS GT because if 2 lines are to the same line then they are to each other. s
55. (continued)
c. Opp. Sides of a are .
d. Trans. Prop. of
e. If 2 lines are to the same line, then they are to each other.
f. If 2 lines are , then the corr. are
g. Trans. Prop. of
h. AAS
i. CPCTC
6-2

6. Properties of Parallelograms
GEOMETRY LESSON 6-2
58. Answers may vary. Sample:
1. LENS and NGTH are (Given)
GTH GNH (Opp of a are .)
3. ENS GNH (Vertical are .)
LEN is supp. to ENS (Cons. in a are suppl.)
ENS GTH (Trans. Prop. of )
E is suppl. to T. (Suppl. of are suppl.)
59. Answers may vary. Sample: In RSTW and XYTZ, R T and
X T because opp of a are . Then R X by the Trans. Prop. of . s s s s s s
6-2

7. Properties of Parallelograms
GEOMETRY LESSON 6-2
60. In RSTW and XYTZ, XY TW and RS TW by the def. of a
. Then XY RS because if 2 lines are to the same line, then they are to each other.
61. AB DC and AD BC by def. of .
and because if 2 lines are , then alt. int are .
because if are each
to , then they are By Def. of bisect, AC bisects DCB.
62. a. Given: 2 sides and the included of ABCD are to the corr. parts of WXYZ. Let A W, AB WX and
62. a. (continued)
AD WZ. Since opp of a are , A C and W
Y. Thus C Y by the Trans. Prop. of Similarly, opp. sides of a are , thus AB CD and WX ZY. Using the Trans. Prop. of , CD ZY. The same can be done to prove BC XY. Since consec of a are suppl., A is suppl. to D, and W is suppl. to Z. Suppls. of are , thus D Z. The same can be done to prove
B X. Therefore, since all corr and sides are , s s s s s s s
6-2

8. Properties of Parallelograms
GEOMETRY LESSON 6-2
62. a. (continued)
ABCD WXYZ.
b. No; opp and sides are not necessarily in a trapezoid.
63. 10
64. 11
69. 42
70. rhombus
71. parallelogram
72. AC DB
73. 49
75. 49 s
6-2