<s>[INST] 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

 [/INST] Yes. This is correct provided you have shown that all yellow triangles are congruent.
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