MEMO 2009 Problem 3

Let $ABCD$ be a convex quadrilateral such that $AB$ and $CD$ are not parallel and $AB=CD$ . The midpoints of the diagonals $AC$ and $BD$ are $E$ and $F$ , respectively. The line $EF$ meets segments $AB$ and $CD$ at $G$ and $H$ , respectively. Show that $\angle AGH = \angle DHG$ .