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Warm Up Given: Diagram as shown Prove: <1 congruent <3 Hint: Think of Supplementary Angles! 1. <ABC is a straight < 2. <1 is supp to < 2 3. <DBE is a straight < 4. <2 is supp to <3 5. <1 congruent to <3 1. Assumed 2. If 2 adjacent <s form a straight <, they are supp 3. Same as 1 4. Same as 2 5. Supplements of the same < are congruent 2.8 Vertical Angles http://www.phschool.com/atschool /academy123/html/bbapplet_wlproblem-431584.html 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 V Y 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. You can assume Vertical Angles! Def: 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 B E 2 4 C D <1 &<2; <3 & <4 are vertical angles. T18: Vertical angles are congruent. 6 5 7 Given: diagram Prove <5 congruent to <7 Hint: use supplementary angles 2.4 problem Therefore <5 <7 Given: <2 congruent to <3 Prove: <1 congruent to <3 1 2 3 4 5 6 m<4 = 2x +5 m<5 = x + 30 Find the m<4 and m<6 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