Transcript PP Prove Angle Pair Relationships Lesson 4.6 for 1-18

Prove Angle Pair Relationships
Lesson 4.6
Page 223
Lesson 4.6
The goal of this lesson is to be able to use
the properties of special pairs of angles.
Adjacent Angles
1. Two angles that share a common vertex and side,
but have no common interior points are called
adjacent angles.
C
D
A
B
ABC is adjacent
to CBD.
Linear Pair
2. Two adjacent angles are a linear pair if their
noncommon sides are opposite rays.
C
ABC + CBD = 180
A
D
B
Theorem 4.3
3. Right Angles Congruence Theorem:
All right angles are congruent.
C
A
B
m ABC = 90
Theorem 4.4
4. Congruent Supplements
If m1 + m2 = 180
Theorem:
If two angles are
and m1 + m3 = 180
supplementary to the
same angle (or to
then m2 = m3.
congruent angles), then they
2  3.
are congruent.
Theorem 4.5
5. Congruent
Complements Theorem:
If m1 + m2 = 90
If two angles are
complementary to the
and m1 + m3 = 90
same angle (or to
then m2 = m3.
congruent angles), then
they are congruent.
2  3.
Linear Pair Postulate:
6. If two angles form a linear pair, then they are
supplementary.
1
2
m1 + m2 = 180
Theorem 4.6
7. Vertical Angles
Congruence Theorem: If m1 + m2 = 180
Vertical angles are
and m1 + m3 = 180
congruent.
then m2 = m3.
1
2
3
2  3.
Example 1
Guided Practice
Example 2
Example 3
Homework Assignment:
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