Comment by globalnode

That is interesting and made me think. Only after following some of the other subcomments did I manage to understand it. Personally, replacing the word similarity ratio with scale factor made all the difference. At first I thought it was a circular argument, relying on pythag to prove pythag but that scale factor is the key actually, and the fact that side lengths scale linearly but the area scales quadratically. It feels like a similar trick we see when adding logarithms gives us multiplication.