# Corresponding angles of $\square ABCD$ and $\square PQRS$ are equal, $AB=PQ$, $CD=SR$, $AD\not\parallel BC$; prove the quadrilaterals congruent

If two quadrilaterals $$ABCD$$ and $$PQRS$$ have angles $$A$$, $$B$$, $$C$$, $$D$$ equal to angles $$P$$, $$Q$$, $$R$$, $$S$$ respectively and $$AB=PQ$$, $$DC=SR$$, and if $$AD$$ is not parallel to $$BC$$, prove that the quadrilaterals are congruent.

What I have done - Given all angles are equal, we have to prove that $$BC=QR$$ and $$AD=PS$$. I have tried using congruency of triangles as follows: $$AB=PQ$$, and $$\angle A$$ is equal to $$\angle P$$. However, I cannot find the third equation to complete the proof.