In a convex quadrilateral $ABCD, \angle A < 90^o, \angle B < 90^o$ and $AB > CD$. 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 $CD$.
Problem
Source: 2018 Singapore Senior round 2 p2
Tags: geometry, parallel, similar triangles, similar