Prove the Following:

Question

Given: Angle PMN is congruent to angle PNM

Prove: Angle CMP is congruent to angle DNP

Answer 1

angle PMN = angle PNM given

angle CMP + angle PMN = 180 definition of supplementary for

angle DNP + angle PNM = 180 linear pairs

angle CMP + angle PMN = 180 transitive / substitution

angle DNP + angle PNM

angle CMP = angle DNP subtraction property of equality