Solution to Puzzle #103: Proof Without Trigonometry

A wonderful puzzle, and the solution is a beautiful one. This was a difficult one, and therefore I did not get as many answers to the puzzle. Abhinav was the first one to send a correct answer – and a correct one, same as the original method. Suman Saraf sent an alternative answer, again a correct one. I got two more answers but they used trigonometry, and hence not reproducing them here.

Here is the answer as stated in the original solution, which I have picked up from The Guardian. Look at the figure below.

Puzzle 103 Solution

Puzzle 103 Solution

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.

Suman sent a similar answer, which is that he extended the graphic, but in a different way and did not use trigonometry. Very well done. Reproducing the answer as sent by Suman in the figure below:

Suman Saraf Puzzle 103 Solution

Suman Saraf Puzzle 103 Solution

Hope you all enjoyed the puzzle!

 

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