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.
Can someone please help?