Midpoints of a quadrilateral

Midpoints of a quadrilateral:[br][br]By moving the corners of a quadrilateral, even producing a self-intersecting shape, the shape generated by connecting the midpoints of each line is always a parallelogram. Can you see why? This can be proved using similar triangles or vectors, among other ways.
Midpoints of a quadrilateral

Information: Midpoints of a quadrilateral