For any quadrilateral, joining the consecutive midpoints of the sides creates a parallelogram

Drag [math]A[/math], [math]B[/math], [math]C[/math], and [math]D[/math] around and see how [math]EFGH[/math] changes.[br][br]Does it still appear to work if [math]ABCD[/math] is [i]convex[/i]?[br]What if [math]ABCD[/math] is not a [i]simple[/i] quadrilateral (i.e. it intersects itself)?[br][br]