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# A square in a trianlge

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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.

Oct 2, 2018
edited by Guest  Oct 3, 2018

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Pease help quick!

Oct 3, 2018
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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.

Oct 3, 2018
#3
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Maybe this is what Melody is referring to: https://web2.0calc.com/questions/a-square-defg-varies-inside-equilateral-triangle

Oct 3, 2018
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Thanks very much guest, that is indeed the same question only not the desired answer.

There was another one more recent that that did not have a picture with it. It had a few different answers.

Melody  Oct 3, 2018