Prove that in quadrilateral MNOP, if MN = OP and MP = NO, then angle PMN = angle NOP.

We are given a quadrilateral $MNOP$ with the following properties:

• $\overline{MN} = \overline{OP}$
• $\overline{MP} = \overline{NO}$

We need to prove that $\angle PMN = \angle NOP$.

Draw the diagonal $\overline{NP}$ in the quadrilateral $MNOP$. This divides the quadrilateral into two triangles: $\triangle MNP$ and $\triangle PON$.

Consider $\triangle MNP$ and $\triangle PON$:

1. $MN = OP$ (Given)
2. $MP = NO$ (Given)
3. $NP = PN$ (Common side to both triangles)

By the Side-Side-Side (SSS) congruence criterion, $\triangle MNP \cong \triangle PON$.

Since $\triangle MNP \cong \triangle PON$, their corresponding angles are equal.
The angle $\angle PMN$ in $\triangle MNP$ corresponds to the angle $\angle NOP$ in $\triangle PON$.
Therefore, $\angle PMN = \angle NOP$.

This completes the proof.

$\boxed{\text{Proven that } \angle PMN = \angle NOP}$