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Three Squares

Problem

Three squares are joined together to create a triangle.

Prove that $a + b + c = 360^o$.


Solution

Consider the following diagram.

The sum of angles around each vertex of the triangle will be $360^o$ and the sum of angles in the triangle $d + e + f = 180^o$.

$\begin{align}\therefore 3 \times 360 &= a + b + c + d + e + f + 6 \times 90\\1080 &= a + b + c + 180 + 540\\\therefore 360 &= a + b + c\end{align}$

Q. E. D.

What are the conditions for $a$, $b$, and $c$ for this result to be true?
What if four squares are joined together to form a quadrilateral?

Problem ID: 317 (07 Apr 2007)     Difficulty: 2 Star

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