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. 3 E B A 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. 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 = 180-55 = 125