Problem #PRU-53644

Problem

Consider a quadrilateral $ABCD$. Choose a point $E$ on side $AB$. A line parallel to the diagonal $AC$ is drawn through $E$ and meets $BC$ at $F$. Then a line parallel to the other diagonal $BD$ is drawn through $F$ and meets $CD$ at $G$. And then a line parallel to the first diagonal $AC$ is drawn through $G$ and meets $DA$ at $H$. Prove the $EH$ is parallel to the diagonal $BD$.