Transcript 2.8 Vertical Angles

Vertical Angles
Lesson 2.8
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.
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.
Vertical Angles: when
ever two lines intersect,
two pairs of vertical
angles are formed.
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.
A
3
1
D
B
E
2
4
C
<1 &<2; <3 & <4 are vertical angles.
Theorem 18:
Vertical angles are congruent.
5
6
7
Given: diagram
Prove <5 congruent to <7
Hint: use

supplementary angles
Back to the last problem, we can use this same
strategy to prove <5
<7.

Given: <2 congruent to <3
Prove: <1 congruent to <3
1. 2  3
2. 1  2
3. 1  3
2
1
3
1. Given
2. Vertical angles are .
3. If s are  to the
same , they are
(Transitive Property)

.
4
m 4 = 2x +5
m 5 = x + 30
Find the m 4
and m 6
6
5
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 <6 = 180-55
= 125