Proving Pythagoras Theorem.

1. Prove Area of [HBK] (blue) = Area of [CBK] (red). 2. Prove Area of [CBL] (green) = Area of [ABK] (yellow). 3. Prove Area of [CBK] (red) = Area of [ABK] (yellow) and thus Area of [CBL] (green) = Area of [HBK] (blue). 4. Therefore, area of the brown rectangle is [math]b^2[/math]. By similar construction, the area of the black rectangle is found to be [math]a^2[/math]. 5. What is your conclusion?