Proving the Pythagorean theorem
We will now prove the Pythagorean theorem:
Statement: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
i.e, If a and b are the legs and c is the hypotenuse then.
Proof: We can prove the theorem algebraically by showing that the area of the big square equals the area of the inner square (hypotenuse squared) plus the area of the four triangles: