If you like this sort of thing, there's a game where you can solve these kinds of proofs: https://www.euclidea.xyz/en/game/packs/Alpha

That is neat, I did not know this method of constructing a gold ratio. Once you have a golden ration it's easy to construct a pentagon (with straight-edge and compass).

I always like the equlateral triangle with the top half removed to for a rombus, the shape is used in the mosaic virus. now I understand my attraction to it, thanks!

Thanks! I didn't know this one either.