prove in three steps by similar triangles pythagorean theorem for general right triangle ABC shown in diagram, that is show a^2+b^2=c^2

Question

w and z are angles. lower case a,b,d,e, and c (c=d+e) are side lengths

Answer 1

step 1. [(d+e)/b]=b/e or b²=e*(d+e)

step 2. [(d+e)/a]=a/d or a²=d*(d+e)

step 3. a²+b²=d*(d+e)+e*(d+e)=(d+e)*(d+e)=(d+e)²=c²

steps 1. &2. are geometry ratios and step 3. is algebra

After drawing right triangle ABC, establish altitude CF from C to Line AB.

(that is shown in the question)

now align the two small triangles and large triangle so the hypotenuses

are all going from bottom right to top left. Angle w on bottom right.