## 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.

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:

Hope you all enjoyed the puzzle!

This entry was posted in Solution and tagged , . Bookmark the permalink.