Vertical Angles

1
Vertical Angles
Lesson 2.8
2
Opposite Rays Two collinear rays that have a
common endpoint and extend in different directions
B
A
C
Ray AB and ray AC are opposite rays.
3
B
A
C
D
Ray BA and Ray CD are not opposite rays.
X
Y
V
U
Ray UV and Ray XY are not opposite rays. NO
common end point.
4
Vertical Angles when ever two lines intersect,
two pairs of vertical angles are formed.
5
Definition Two angles are vertical angles if
the rays forming the sides of one angle and the
rays forming the sides of the other are opposite
rays.
E
3
B
A
2
1
4
C
D
lt1 lt2 lt3 lt4 are vertical angles.
6
Theorem 18 Vertical angles are congruent.
6
7
5
Given diagram Prove lt5 congruent to lt7
Hint use supplementary angles
7
Back to the last problem, we can use this same
strategy to prove lt5 lt7.
8
1
Given lt2 congruent to lt3 Prove lt1 congruent
to lt3
2
3

1. Given
2. Vertical angles are ?.
3. If ?s are ? to the same ?, they are ? .
   (Transitive Property)

1. ?2 ? ?3
2. ?1 ? ?2
3. ?1 ? ?3

9
5
4
6
m ?4 2x 5 m ?5 x 30 Find the m ?4 and m ?6
10
Vertical angles are congruent so just set them
equal to each other and solve for x. REMEMBER to
plug x back in to find the angle.
The measure of lt6 180-55 125