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
Solution 1:
Yes. This is correct provided you have shown that all yellow triangles are congruent.