Answer
By AAS, $\triangle MNP \cong \triangle QRP$
Work Step by Step
Angle: $\angle MNP \cong \angle RQP$ (This is given in the question.)
Angle: $\angle MPN \cong \angle RPQ$, since they are opposite angles
Side: $\overline{MP} \cong \overline{RP}$, since P is the midpoint of $\overline{MR}$
Therefore, by AAS, $\triangle MNP \cong \triangle QRP$
