Congruent+Supplements+Theorem

Congruent Supplements Theorem Katherine King, Emmi Shearman, Emma Wheatley, Makenzie Carter

Congruent Supplements Theorem: if two angles are supplementary to the same angle, then they are congruent Emmi Shearman 1) Angle 1 and angle 2 are supplementary Angle 1 and angle 3 are supplementary Are angles 2 and 3 congruent? 2) Angles 1 and 2 are not supplementary Angles 1 and 3 are supplementary Are angles 2 and 3 congruent?

Answers: 1) yes 2) no


 * __Katherine King__**

Given - Angle 1 is supplement to Angle 2 Angle 3 is supplement to Angle 4 Angle 2 is Congruent to Angle 4

Prove - Angle 1 is Congruent to Angle 3

Answer Measure of Angle 1 + Measure of Angle 2 = 180 degrees Def. of Supplementary Angles Measure of Angle 3 + Measure of Angle 4 = 180 degrees Def. of Supplementary Angles Measure of Angle 1 + Measure of Angle 2 = Measure of Angle 3 + Measure of Angle 4 Transitive Property of Equality Angle 2 is Congruent to Angle 4 Given Measure of Angle 2 = Measure of Angle 4 Def. of Congruence Measure of Angle 1 + Measure of Angle 2 = Measure of Angle 3 + Measure of Angle 2 Substitution Property of Equality Measure of Angle 1 = Measure of Angle 3 Subtraction Property of Equality Angle 1 is Congruent to Angle 3 Def. of Congruence