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Proving Congruent Angles using Supplementary Angles

In this problem, we are given a diagram and need to prove the congruence of certain angles using the concept of supplementary angles. We use the properties of vertical angles and solve for the unknown angle measure.

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Proving Congruent Angles using Supplementary Angles

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  1. Warm Up Given: Diagram as shown Prove: <1 congruent <3 Hint: Think of Supplementary Angles! • <ABC is a straight < 1. Assumed • <1 is supp to < 2 2. If 2 adjacent <s form • a straight <, they are supp 3. <DBE is a straight < 3. Same as 1 4. <2 is supp to <3 4. Same as 2 5. <1 congruent to <3 5. Supplements of the same < are congruent

  2. 2.8 Vertical Angles http://www.phschool.com/atschool/academy123/html/bbapplet_wl-problem-431584.html

  3. 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.

  4. 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.

  5. Vertical Angles: when ever two lines intersect, two pairs of vertical angles are formed. You can assume Vertical Angles!

  6. 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. 3 E B A 2 1 4 C D <1 &<2; <3 & <4 are vertical angles.

  7. T18: Vertical angles are congruent. 6 7 5 Given: diagram Prove <5 congruent to <7 Hint: use supplementary angles

  8. 2.4 problem Therefore <5 <7

  9. Given: <2 congruent to <3 Prove: <1 congruent to <3 1 2 3

  10. 5 4 6 m<4 = 2x +5 m<5 = x + 30 Find the m<4 and m<6

  11. 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

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