I'm having a lot of trouble on a problem.
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. 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 BC remains constant.
Please do not use the law of sines in your proof.
+118609 I saw this answered not too long ago. Perhaps someone can find the older version?
I seem to recall that it was a long answer, maybe Heureka answered it but I am not sure. 
