Question 30
Let $E$ and $F$ be the points on the sides $AB$ and $AD$ of a convex quadrilateral $ABCD$, such that $EF$ is parallel to $BD$. The segment $CE$ intersects the diagonal $BD$ at $G$, while the segment $CF$ intersects the diagonal $BD$ at $H$. Prove: if $AGCH$ is a parallelogram, then $ABCD$ is a parallelogram as well.