Quadrilateral Problem

Date: 8 May 1995 02:14:59 -0400
From: Andrei Gheorghe
Subject: Squares problem

Hello there,

I have this problem for you.  If you can solve it, please let me 
know.  I've been working on it and no results.
        
Let ABCD be a convex quadrilateral and M, N, P, Q points on AB, BC, 
CD, DA respectively, such as BM = CN = DP = AQ. Prove that, if MNPQ 
is a square then ABCD is a square.

Date: 9 Jun 1995 14:49:42 -0400
From: Dr. Ken
Subject: Re: Squares problem

Hello there!

We're finally getting around to your problem.  I've created a couple of nice
sketches using the Geometer's Sketchpad, and I've put them at the following
addresses: http://excalibur.swarthmore.edu/squares.gsp    and
http://excalibur.swarthmore.edu/squares2.gsp   .  Check them out!  If you don't
have a copy of the Geometer's sketchpad, you can download a demo version of
it from http://mathforum.org   .

If you can, take a look at these sketches, and see if they help you figure
out how to construct a traditional proof.  If not, write back to us and
we'll try to get you on the right track.

-K