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)
![](https://gradesaver.s3.amazonaws.com/uploads/solution/99f0920a-6b53-43e2-bd7e-b43b8a625de2/steps_image/small_1480973084.png?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T021538Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=eda298274534abd6698745b07ec98ce4a5ad122357bd52b2498b6e0f77ef3a78)