KöMaL 2010 C1044

The diagonals of a convex quadrilateral ABCD intersect at point $M$. Extend diagonal $AC$beyond $A$ by the length of $MC$, and extend diagonal $BD$ beyond $B$ by the length of $MD$ to get the points $E$ and $F$. Prove that $EF$ is parallel to a midline of the quadrilateral.