Question 10
Let $E$ and $F$ be points on the sides $AB$ and $AD$ of a convex quadrilateral $ABCD$ such that $EF \parallel BD$. The segment $CE$ meets the diagonal $BD$ at the point $G$, and the segment $CF$ meets the diagonal $BD$ at the point $H$. Prove: if $AGCH$ is a parallelogram, then $ABCD$ is also a parallelogram.