20. The proof that many attribute to Pythagoras himself (i.e., the "ox-killer proof"):
Begin with identical squares of side $b + c$, decomposed as shown.
(a) Show the area of the left-hand square is $2bc + b^2 + c^2$.
(b) Prove that the inner figure on the right is itself a square.
(c) Show the area of the right-hand square is $2bc + a^2$.
(d) Now prove the Pythagorean Theorem from these preliminaries.