The figures shown can be used to see why the Pythagorean Theorem is true. Both large squares have the same area, but they are broken up in different ways. When the sum of the four areas in Square F is set equal to the sum of the 5 areas in Square G, the result is $a^2+b^2=c^2$, where $c$ is the hypotenuse of the triangles in Square G and also the side length of the square in the middle. 

First of two squares of the same area. This square is divided into the following: A square with side lengths “a”. Two rectangles with side lengths “a” and “b”. A square with side lengths “b”.

Second of two squares of the same area. This square is divided into the following: Four identical triangles on each corner of the square with sides labeled “a” and “b”. A square in the center with unlabeled side lengths.

This is true for any right triangle. If the legs are $a$ and $b$ and the hypotenuse is $c$, then $a^2+b^2=c^2$.

For example, to find the length of side $c$ in this right triangle, we know that $24^2+7^2=c^2$. The solution to this equation (and the length of the side) is $c=25$.