BG-MO 1979 Problem 5

A convex pentagon $ABCDE$ satisfies $AB=BC=CA$ and $CD=DE=EC$ . Let $S$ be the center of the equilateral triangle $ABC$ and $M$ and $N$ be the midpoints of $BD$ and $AE$ , respectively. Prove that the triangles $SME$ and $SND$ are similar.