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

A square DEFG varies inside equilateral triangle ABC, so that E always lies on side line AB, F always lies on side line BC, and G always lies on side line AC. The point D starts on side line AB, and ends on side line AC. The diagram below shows the initial position of square DEFG, an intermediate position, and the final position.

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

Thanks for the help!