Pythagoras Theorem

Consider a large square ABCD. Points W, X, Y, Z lie on sides AD, AB, BC, CD respectively.

Four identical right-angled triangles are formed inside the square. Each triangle has base a, height b, and hypotenuse c.

These triangles are arranged so that their hypotenuses form a tilted inner square WXYZ.

The area of the large square ABCD is = (a + b)²

Additionally, Area of square ABCD = Area of 4 triangles + Area of square WXYZ

Area of 4 triangles = 4 × ½ab = 2ab

Area of square WXYZ = c²

(a + b)² = 2ab + c²

a² + 2ab + b² = 2ab + c²

a² + b² = c²

Hence, the Pythagoras Theorem is proved.

a² + b² = c²