# Chapter 3 - Section 3.2 - Corresponding Parts of Congruent Triangles - Exercises - Page 152: 31

- First, prove that $\triangle MQP\cong\triangle PNM$ - Then, by CPCTC, $\angle 3\cong\angle 4$ - Then, since 2 interior alternate angles are congruent, $\overline{MQ}\parallel\overline{NP}$

#### Work Step by Step

*PLANNING: - First, prove that $\triangle MQP\cong\triangle PNM$ - Then, by CPCTC, $\angle 3\cong\angle 4$ - Then, since 2 interior alternate angles are congruent, $\overline{MQ}\parallel\overline{NP}$ 1) $\angle 2\cong\angle 1$. (Given) 2) $\overline{QP}\cong\overline{NM}$ (Given) 3) $\overline{MP}\cong\overline{PM}$ (Identity) So now we have 2 lines and the included angle of $\triangle MQP$ are congruent with 2 corresponding lines and the included angle of $\triangle PNM$ 4) $\triangle MQP\cong\triangle PNM$ (SAS) 5) $\angle 3\cong\angle 4$ (CPCTC) 6) $\overline{MQ}\parallel\overline{NP}$ (if 2 interior alternate angles for 2 lines are congruent, these 2 lines are parallel)

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