Todd has created the following diagram to prove the Pythagorean theorem. He drew right Δ A B C with leg lengths a and b and hypotenuse length c. Then he drew altitude C Z to the hypotenuse. He determines that c/a=a/x and c/b=b/y. Then he determines that c x=a² and c y=b². What is the next step in proving the theorem?

c²=a²+b²
c x=c y
c x+c y=a²+b²
c(x+y)=a²+b²