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LESSON
3.2
Answers for the lesson “Use Parallel Lines
and Transversals”
Skill Practice
11. Alternate Interior Angles
Theorem
1. Sample:
12. Consecutive Interior Angles
Theorem
1
2
13. Alternate Exterior Angles
Theorem
14. Corresponding Angles Postulate
15. Alternate Exterior Angles
2. congruent: alternate interior
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angles, alternate exterior angles,
corresponding angles, vertical
angles; supplementary: adjacent
angles, consecutive interior
angles, exterior angles on the
same side of the transversal.
3. C
4. 658; Vertical Angles Congruence
Theorem
5. 1108; Alternate Exterior Angles
Theorem
6. 718; Alternate Interior Angles
Theorem
7. 638; Consecutive Interior Angles
Theorem
8. 548; Alternate Exterior Angles
Theorem
16. Consecutive Interior Angles
Theorem
17. mŽ1 5 1508, mŽ2 5 1508;
Corresponding Angles
Postulate, Vertical Angles
Congruence Theorem
18. mŽ1 5 1408, mŽ2 5 408;
Alternate Interior Angles
Theorem, Consecutive Interior
Angles Theorem
19. mŽ1 5 1228, mŽ2 5 588;
Alternate Interior Angles
Theorem, Consecutive Interior
Angles Theorem
20. The lines are not known to be
parallel, therefore Ž9 and Ž10
are not necessarily congruent.
Theorem
9. Corresponding Angles Postulate
10. Alternate Interior Angles
Theorem
Geometry
Answer Transparencies for Checking Homework
63
21. Sample answer: Ž1 > Ž4 by the
26. Sample answer: ŽBAD and
Alternate Exterior Angles
Theorem; Ž1 > Ž2 >Ž3 >Ž4
by Vertical Angles Congruence
Theorem, Alternate Interior
Angles Theorem, and the
Transitive Property of Angle
Congruence.
ŽABC, ŽCDA and ŽDCB
22. mŽ1 5 1008, Consecutive
Interior Angles Theorem;
mŽ2 5 808, Consecutive Interior
Angles Theorem; mŽ3 5 1008,
Consecutive Interior Angles
Theorem
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23. mŽ1 5 908, supplementary to the
right angle by the Consecutive
Interior Angles Theorem;
mŽ3 5 658, it forms a linear pair
with the angle measuring 1158;
mŽ2 5 1158, supplementary to
Ž3 by the Consecutive Interior
Angles Theorem
24. mŽ3 5 478, supplementary to the
27. 45, 85
28. 45, 20
29. 65, 60
30. 20, 10
31. 13, 12
32. 10, 25
33. B
34.
M
P
Q
N
ŽM and ŽQ, ŽP and ŽN.
Sample answer: ŽP is
supplementary to ŽM and
ŽQ, therefore by the Congruent
Supplements Theorem they are
congruent; ŽQ is supplementary
to ŽP and ŽN, therefore by the
Congruent Supplements Theorem
they are congruent.
35. 65, 10
36. 8, 10
angle measuring 1338 by the
Consecutive Interior Angles
Theorem; mŽ2 5 1338, it forms a
linear pair with Ž3; mŽ1 5 478,
mŽ1 5 mŽ3 by the Alternate
Interior Angles Theorem
25. Sample answer:ŽBAC and
ŽDCA, ŽABD and ŽCDB
Geometry
Answer Transparencies for Checking Homework
64
Problem Solving
41. Statements (Reason)
1. n i p
37. Statements (Reason)
1. p i q
2. Ž1 > Ž3
(Given)
(Corresponding
Angles Postulate)
3. Ž3 > Ž2
(Vertical Angles
Congruence Theorem)
4. Ž1 > Ž2 (Transitive Property
of Angle Congruence)
38. a. Ž4, Ž5, Ž8
b. 708
39. a. yes; Ž1 and Ž5, Ž2 and Ž6;
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yes; Ž1 and Ž2, Ž1 and Ž6,
Ž2 and Ž5, Ž5 and Ž6
b. Sample answer: The
transversal stays parallel to
the floor.
40. a. 708, 1108
b. Sample answer: Ž1 and
Ž2 are corresponding angles
and therefore congruent. Ž1
and Ž3 are supplementary so
by substitution Ž2 and Ž3 are
supplementary, so ŽABC is a
straight angle.
c. Yes; steeper. Sample answer:
The points are collinear, if
mŽ1 is 608, the angle is
smaller and the line becomes
steeper.
2. Ž1 > Ž3
(Given)
(Alternate Interior
Angles Theorem)
3. mŽ1 5 mŽ3 (Definition of
congruent angles)
4. Ž3 and Ž2 are supplementary.
(Linear Pair Postulate)
5. mŽ2 1 mŽ3 5 1808
(Def. of supplementary angles)
6. mŽ1 1 mŽ2 5 1808
(Substitution Property)
7. Ž1 and Ž2 are supplementary.
(Def. of supplementary angles)
42. Statements (Reason)
1. t > r; r i s
(Given)
2. Ž1 is a right angle.
(Def. of perpendicular lines)
3. mŽ1 5 908
4. Ž1 > Ž2
(Definition of
right angle)
(Corresponding
Angles Postulate)
5. mŽ1 5 mŽ2 (Definition of
congruent angles)
6. mŽ2 5 908
(Substitution)
7. Ž2 is a right angle.
(Definition of right angle)
8. t > s
(Definition of
perpendicular lines)
Geometry
Answer Transparencies for Checking Homework
65
43. 608. Sample answer: Ž4 > Ž2
Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved.
by the Alternate Interior Angles
Theorem, Ž2 > Ž3 by definition
of angle bisector, Ž5 > Ž1 by
Corresponding Angles Postulate,
Ž4 > Ž5 is given, so Ž1 > Ž2 >
Ž3 > Ž4 > Ž5. Since
mŽ1 1 mŽ2 1 mŽ3 5 1808,
they must each be 608.
Geometry
Answer Transparencies for Checking Homework
66