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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