What is your favorite proof of the Pythagorean Theorem? Why?

Question

My favorite is Euclid's original proof for two reasons:

First, it requires minimal raw material. It only needs the result that the area of a triangle is half the area of a rectangle with the same base and altitude.

Second, it gives additional information, in that it shows how to divide the square on the hypotenuse into two rectangles each of which is equal in area to one of the squares on the legs.

So, what's yours?

Answer 1

Let $ABC$ be a right triangle, with right angle at $A$. Let $H$ be the foot of the altitude from $A$. Triangles $ABH$, $ACH$ and $ABC$ are similar, being their areas proportional to the square of the hypothenuses, that is, $$a^2=b^2+c^2$$

For brevity.

Answer 2

I would say Garfield's proof, which shows and two different ways to represent the area of the trapezoid. In that site it is the last one. Plus, the guy was one of our presidents at one point!