# Pythagoras Theorem Proof

Is my logic correct below to prove the Pythagoras Theorem? Thanks.

Area Rectangle R \begin{align*} R &= WL\\ &=(2a+b)(2b+a)\\ &=4ab+2a^2+2b^2+ab\\ &=5ab+2a^2+2b^2 \end{align*}

Total Area Yellow Triangles T \begin{align*} T &= 10(\frac{ab}{2})\\ &=5ab \end{align*}

Calculate Area $$c^2$$

\begin{align*} c^2 &= R-T-a^2-b^2 \\ &=5ab+2a^2+2b^2-5ab-a^2-b^2\\ &=a^2+b^2 \end{align*}

Proof by rearrangement

• SAS (side-angle-side) congruency is sufficient. They each have two smaller sides $a$ and $b$ and one included right angle. – cosmo5 Nov 29 '20 at 20:47