Three Squares Problem

  • Context: High School 
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bob012345
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TL;DR
Using only elementary geometry (not even trigonometry), prove that angle C in the figure equals the sum of angles A and B.
This problem is another from Martin Gardner’s book Mathematical Circus but originates from a fourth grade extra credit question in a Moscow school long ago. It makes me wonder how America won the Space Race! The problem statement is simply;

Using only elementary geometry (not even trigonometry), prove that angle C in the figure equals the sum of angles A and B.

IMG_4901.webp


There are apparently dozens of proofs of this so I suggest just showing your solution and others can come up with different solutions. I selected High School because it probably is at least that level for today’s readers. Have fun!
 

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