# The middles of the sides of any quadrilateral make a parallelogram

Submitted by Isoscel on Sat, 10/27/2007 - 00:14.

The middles of the sides of any quadrilateral are the corners of a parallelogram.

Proof:

We draw a diagonal of the big quadrilateral.

We notice that the diagonal is parallel and twice the size of two opposing sides of the smaller quadrilateral.

This means that the two opposing sides of the smaller quadrilateral are equal and parallel.

So the smaller quadrilateral is a parallelogram.

(try to drag the green corners)