Answer
1) Prove that $\triangle MQP\cong\triangle NPQ$ by method SAS.
2) Then, by CPCTC, $\overline{MP}\cong\overline{NQ}$
Work Step by Step
*PLANNING:
- First, prove that $\triangle MQP\cong\triangle NPQ$
- Then, by CPCTC, $\overline{MP}\cong\overline{NQ}$
1) $\angle MQP$ and $\angle NPQ$ are right $\angle$s. (Given)
2) $\angle MQP\cong\angle NPQ$ (two corresponding right angles are congruent)
3) $\overline{MQ}\cong\overline{NP}$ (Given)
4) $\overline{QP}\cong\overline{PQ}$ (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 $\triangle NPQ$
5) $\triangle MQP\cong\triangle NPQ$ (SAS)
6) $\overline{MP}\cong\overline{NQ}$ (CPCTC)
