Pythagoras's Theorem/Proof 2

Proof

 * Pythagoras2.png

We have:
 * $\dfrac b c = \dfrac d b$

and:
 * $\dfrac a c = \dfrac e a$

using the fact that all the triangles involved are similar.

That is:
 * $b^2 = c d$
 * $a^2 = c e$

Adding, we now get:
 * $a^2 + b^2 = c d + c e = c \left({d + e}\right) = c^2$