Looking at the diagram, the figure is made up of a small square, four right triangles, and a large square. The steps for the proof:
- The area of the large square = (c)(c) = c^2.
- The area of the 4 triangles = 4(.5ab) = 2ab.
- The area of the small square = (b - a)(b - a) = b^2 - 2ab + a^2.
- The area of the large square equals the area of four right triangles plus the area of
the small square.
c^2 = (2ab) + (b^2 - 2ab + a^2)
c^2 = b^2 + a^2
- Therefore, the sum of the squares of sides of a right triangle equals the square of