Pythagorean Theorem Proof

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. To prove this, you can arrange four identical right triangles within a square. The area of the large square (formed by the hypotenuse) is calculated in two ways: by the square of the hypotenuse and by adding the areas of the four triangles plus the area of the smaller center square. Both methods yield the same result, confirming the theorem's validity.