Pythagorean Theorem Proof

Both Areas Must Be Equal

The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as:

(a+b)(a+b) = c² + 2ab

NOW, let us rearrange this to see if we can get the Pythagorean theorem:

Start with:

(a+b)(a+b) = c² + 2ab

Expand (a+b)(a+b):

a² + 2ab + b² = c² + 2ab

Subtract 2ab from both sides:

a² + b² = c²

DONE!

Now we can see why the Pythagorean theorem works ... and it is actually a proof of the theorem.

This proof came from China over 2000 years ago!

There are many more proofs of the Pythagorean theorem, but this one works neatly.