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

Guest Mar 14, 2018
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It says...

"The diagram below shows the initial position of square DEFG,  an intermediate position, and the final position."

 

Where is the diagram?

Melody  Mar 14, 2018

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