Rays Through the Squares

 

Solution

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One of the proofs to this problem is shown in the illustration. 

Let's construct the additional squares indicated by dotted lines. It is clear from the illustration that angle C is the sum of angles A and D. Angle B equals angle D because they are corresponding angles of similar right triangles (with the respective legs in the 1:2 proportion). That means B can be substituted for D, which automatically makes the C equals the sum of A and B.

 
Last Updated: August 18, 2008  |  Posted: January 18, 2004
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