We built b ^ 2 and c ^ 2 above a ^ 2. We draw a parallel to c in b ^ 2. call m and n to the legs close to b. draw AH = m, BO = n. draw FO perpendicular to m and n.
We build DKL = EFG, AJI = BON
then
EFDM + AHOB = b ^ 2
GHJI + KLMN = a ^ 2
c^2 = a^2 + b^2
