Question 110
In a convex quadrilateral $ABCD$, $\angle A \lt 90^\circ$, $\angle B \lt 90^\circ$ and $AB \gt CD$. Points $P$ and $Q$ are on the segments $BC$ and $AD$ respectively. Suppose the triangles $APD$ and $BQC$ are similar. Prove that $AB$ is parallel to $CD$.