Download 8-22-12 Lesson 4_6 Angle Pair Relationships

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Transcript 
Lesson 4.6 Angle Pair
Relationships
Page 223
Lesson 4.6
Adjacent Angles
1. Two angles that share a common vertex and side, but
have no common interior points are adjacent angles.
C
D
A
B
ABC is adjacent
to CBD.
Linear Pair
Two adjacent angles are a linear pair if their
noncommon sides are opposite rays.
C
ABC + CBD = 180
A
D
B
Theorem 4.3
Right Angles Congruence Theorem:
All right angles are congruent.
C
ABC = 90
A
B
Theorem 4.4
Congruent Supplements
Theorem:
If m1 + m2 = 180
If two angles are
supplementary to the and m1 + m3 = 180
same
then m2 = m3.
angle (or to congruent
angles), then they are
congruent.
2
3.
 
Theorem 4.5
Congruent Complements
Theorem:
If m1 + m2 = 90
If two angles are
supplementary to the and m1 + m3 = 90
same
then m2 = m3.
angle (or to congruent
angles), then they are
congruent.
2  3.
Linear Pair Postulate:
If two angles form a linear pair, then they are
supplementary.
1
2
m1 + m2 = 180
Theorem 4.6
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
Find the other angles as well.
Example 3
Guided Practice #8
Guided Practice #9
Homework 4.6
page 225
1 - 14
True/False
#5 Make a sketch of the given information.
Label all angles which can be determined.
#6 Make a sketch of the given information.
Label all angles which can be determined.
#7 Make a sketch of the given information.
Label all angles which can be determined.
#8 Make a sketch of the given information.
Label all angles which can be determined.
#9 Make a sketch of the given information.
Label all angles which can be determined.
#10 Make a sketch of the given information.
Label all angles which can be determined.
#11 Find the value of the variables and the
measure of each angle in the diagram.
#12 Find the value of the variables and the
measure of each angle in the diagram.
#13 Find the value of the variables and the
measure of each angle in the diagram.
#14 Find the value of the variables and the
measure of each angle in the diagram.
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