BALKAN-SL 2009 G5

Let $ABCD$ be a convex quadrilateral and $S$ an arbitrary point in its interior. Let also $E$ be the symmetric point of $S$ with respect to the midpoint $K$ of the side $AB$ and let $Z$ be the symmetric point of $S$ with respect to the midpoint $L$ of the side $CD$ . Prove that $(AECZ) = (EBZD) = (ABCD)$ .