Answer
1) Show that $\overline{RM}\cong\overline{RQ}$
2) Show that $\angle M\cong\angle Q$
3) Show that $\angle PRQ\cong\angle NRM$
4) Use method ASA to prove triangles congruent.
Work Step by Step
1) It is given that $\overline{PN}$ bisects $\overline{MQ}$ at R.
As a result, $\overline{PN}$ cuts $\overline{MQ}$ into 2 equal parts $\overline{RM}$ and $\overline{RQ}$.
Therefore, $\overline{RM}\cong\overline{RQ}$.
2) $\angle M$ and $\angle Q$ are both right angles, so $\angle M\cong\angle Q$.
3) Since $\overline{PN}$ intersects $\overline{MQ}$, $\angle PRQ\cong\angle NRM$.
Now we have 2 angles and the included side of $\triangle PRQ$ are congruent with 2 corresponding angles and the included side of $\triangle NRM$.
That means according to method ASA, $\triangle PRQ\cong\triangle NRM$.
