KöMaL 2006 B3894

The lines of the legs $AB$ and $CD$ of a trapezium ABCD intersect at the point $M$. A line $e$ passing through $M$ intersects the line $AD$ at a point $E$ different from $A$ and $D$, and it intersects the line $BC$ at $F$. The intersection of the diagonals is constructed in each of the trapezia ABFE and CDEF , denote them by $P$ and $Q$. Show that $PQ$ is parallel to the bases of the trapezia.