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

• See also Bhaskara's proof. – Oscar Lanzi Nov 30 '20 at 0:43
• Bhaskara Proof is from cut-the-knot.org/pythagoras Proof #3 Is my proof new or already discovered? Thanks! – vengy Nov 30 '20 at 0:48
• For something as worked over as the Pythagorean Theorem, assume it's already discovered. A very extensive literature search would be needed to prove otherwise. – Oscar Lanzi Nov 30 '20 at 0:55
• True. It seems similar to Proof #87 from cut-the-knot.org/pythagoras – vengy Nov 30 '20 at 3:02

• 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