A square DEFG varies inside equilateral triangle ABC, so that E always lies on side AB, F always lies on side BC, and G always lies

A square DEFG  varies inside equilateral triangle ABC, so that E always lies on side AB, F always lies on side BC, and G  always lies on side AC.  The point D  starts on side AB and ends on side AC. 

 

Show that as square DEFG varies, the height of point D  above BC  remains constant.