Answer
- 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)
