Think of each side of a right triangle as also being a side of a square that's
attached to the triangle. The area of a square is any side multiplied by itself. (For
example, a x a = a^{2}).

To show that a^{2 }+ b^{2} = c^{2}, follow
these steps:

Click here to get a right triangle on grid paper that you can print. You'll also need
scissors, and a ruler.

Cut out the triangle.

Make three squares with sides that are equal to each side of the triangle.
Begin with side a. Measure the length of side a. On the blank
piece of grid paper, draw a square with sides that are the same length as side
a. Label this square a^{2}. Repeat these steps to
create squares for sides b and c. (If you don't have a
ruler, just use the triangle as a guide; trace the length of one side, and then
draw three more sides of the same length to make a square.)

Cut out the squares. Place each square next to the corresponding sides of
the triangle.

Now show that a^{2 }+ b^{2} = c^{2}. Place
the squares made from sides a and b on top of square c.
You will have to cut one of the squares to get a perfect fit.

Congratulations! You've shown that the Pythagorean theorem works! But how can
you use it?