Pythagorean Theorem

Make a diagram like this: 

The area of the entire square is $(a+b)^2 = a^2 + b^2 + 2ab$

The area can also be represented as the sum of the area of the 4 triangles and the square in the middle: $c^2 + 2ab$

Since they both represent the area of the square, we have the equation $a^2 + b^2 + 2ab = c^2 + 2ab$

Subtracting 2ab from both sides gives us $\color{brown}\boxed{a^2 + b^2 = c^2}$