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A Square Triangulation (Posted on 2005-01-31) Difficulty: 3 of 5
Is it possible to cut a square into seven isosceles right triangles, no two of which are congruent?

See The Solution Submitted by David Shin    
Rating: 3.6667 (3 votes)

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re(2): Solution (spoilers) and a challenge. Comment 4 of 4 |
(In reply to re: Solution (spoilers) by owl)

I started off with the triangle taking up half the square.  I decided that since there were seven noncongruent triangles, something weird had to happen with the triangles touching the main diagonal.  What came to mind is have one leg take up part of it, and for the other part, have a triangles hypotenuse.

I next tried a triangle G_F (_ is a point on EF), but I couldn't get the rectangle at the bottom to split into 3 noncongruent triangles.  My next attempt had FHE, and the others fell into place.  My initial reaction was, "This can't be the right solution.  I'm not that smart." so I checked the lengths of the sides to make sure.  And they all checked out.

My apologies go out to David Shin, whose problem I spoiled too soon.  As reparations, I challenge anyone to find another method. (rotations and reflections don't count) or to prove there is no other way.

  Posted by Dustin on 2005-02-01 14:54:49
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