BD-BDMO 2013 Problem 1

Higher Secondary P1

A polygon is called degenerate if one of its vertices falls on a line that joins its neighboring two vertices. In a pentagon $ABCDE$ , $AB=AE$ , $BC=DE$ , $P$ and $Q$ are midpoints of $AE$ and $AB$ respectively. $PQ||CD$ , $BD$ is perpendicular to both $AB$ and $DE$ . Prove that $ABCDE$ is a degenerate pentagon.