If M1, M2, M3, M4 are the midpoints of consecutive sides of square WXYZ, then each side of the new quadrilateral equals half a diagonal of the original (for example, M2−M1=(C−A)/2), so all four sides are equal and each side is parallel to a diagonal. Because the diagonals of a square are equal in length and perpendicular, adjacent sides of the midpoint quadrilateral are equal and perpendicular, so the figure is a square.