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. 3 E A B 2 1 4 C D
<1 &<2; <3 & <4 are vertical angles.

6. Theorem 18: Vertical angles are congruent.6 7 5
Given: diagram
Prove <5 congruent to <7
Hint: use supplementary angles

7. Back to the last problem, we can use this same strategy to prove <5 <7.

8. If s are  to the same , they are  . (Transitive Property) 2  3 1
Given: <2 congruent to <3
Prove: <1 congruent to <3 2 3
Given
Vertical angles are .
If s are  to the same , they are  . (Transitive Property)
2  3
1  2
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 <6 =
= 125