Let the quadrilateral of this space be ABCD edge, and the midpoints of AB CB CD AD are E, F, G and H respectively.

Because e and h are the midpoint of AB and AD ad respectively.

So EH is the center line of triangle ABD.

So EH//BD and EH= 1/2BD.

In the same way, we can get FG//BD, FG= 1/2BD.

So EH//FG and EH=BD.

So the quadrilateral EHGF is a parallelogram.