Geo_Book_Answers

LESSON 13.2
1. Linear Pair Postulate
2. Parallel Postulate, Angle Addition Postulate,
Linear Pair Postulate, Corresponding Angles
Postulate
3. Parallel Postulate
4. Perpendicular Postulate
5.
2 1
Use the definition of supplementary angles and the
substitution property to get m1 m1 180°.
Then use the division property and the definition
of a right angle.
6.
1 2 4
3
Use the definition of supplementary angles and the
transitive property to get m1 m2 m3
m4. Then use the substitution property and the
subtraction property to get m1 m4.
7.
1 2
Use the definition of a right angle and the
transitive property to get m1 m2. Then use
the definition of congruence to get 1 2.
8.
3 1
3
Use the VA Theorem and the transitive property to
get 1 3. Therefore the lines are parallel by the
CA Postulate.
9.
3 2
3
2
1
1
1
Use the VA Theorem and the CA Postulate to get
1 3 and 2 3. Then use the transitive
property to get 1 2.
2
2
10.
2
3
Use the VA Theorem and the transitive property to
get 3 4. Therefore the lines are parallel by the
Converse of the AIA Theorem.
11.
3 Use the Linear Pair Postulate and the definition of
supplementary angles to get m1 m3 180°.
Then use the CA Postulate and the substitution
property to get m1 m2 180°.
12.
3 3 1
Use the Linear Pair Postulate and the definition of
supplementary angles to get m1 m3
m1 m2. Then use the subtraction property
and the Converse of the AIA Theorem to get
1 2 .
13.
A
1
B 2
3
4
2
2
1
3
1
3
Construct a transversal across lines 1 and 2 ;it
will intersect line 3 by the Parallel Postulate. Use
the Interior Supplements Theorem and the
definition of supplementary angles to get m1
m2 180°. Use the CA Postulate and the
substitution property to get m1 m3 180°.
Therefore 1 3 by the Converse of the Interior
Supplements Theorem.
1
1
1
1
2
3
2
2
2
ANSWERS TO EXERCISES 145
Answers to Exercises