1. Vertical Angles Lesson 2.8

2. Opposite Rays: Two collinear rays that have a common endpoint and extend in different directions BAC Ray AB and ray AC are opposite rays.

3. BACD Ray BA and Ray CD are not opposite rays. VU XY 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. A B E D C 1 2 4 3 <1 &<2; <3 & <4 are vertical angles.

6. Theorem 18: Vertical angles are congruent. 5 6 7 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. 1.2  3 2.1  2 3.1  3 1.Given 2.Vertical angles are . 3.If s are  to the same , they are . (Transitive Property) 1 2 3 Given: <2 congruent to <3 Prove: <1 congruent to <3

9. 4 5 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 = 180-55 = 125