Question 16
Let $ABCD$ be a parallelogram and let $E$, $F$, $G$ and $H$ be the midpoints of the sides $AB$, $BC$, $CD$ and $DA$, respectively. If $BH \cap AC = I$, $BD \cap EC = J$, $AC \cap DF = K$ and $AG \cap BD = L$, then prove that the quadrilateral $IJKL$ is a parallelogram.