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February 28th, 2017, 07:34 AM  #1 
Newbie Joined: Oct 2015 From: Eskişehir Posts: 11 Thanks: 0  Proof of four triangles with equal area.
I have been working on proofs without words, but I have a bit of a problem about Steven Snover's proof. It proves that these four triangles have equal area. Proof comes from rotation, but I couldn't get it. Last edited by skipjack; February 28th, 2017 at 08:36 AM. 
February 28th, 2017, 08:22 AM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 227 Thanks: 122 Math Focus: Dynamical systems, analytic function theory, numerics 
Here is a hint. The outside triangles each have 2 sides equal in length to 2 sides of the inner triangle and the angle between these sides is complimentary to the corresponding angle of the inner triangle.

February 28th, 2017, 08:45 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,247 Thanks: 1439 
Each particular rotated triangle aligns after rotation with the central triangle. The two triangles have the same height and the corresponding base lengths are the same, so the triangles have equal area.


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