A kid thinking through a geometry puzzle

My older son was working in Art of Problem Solving’s geometry book this morning.  When I asked him what he wanted to talk about for today’s movie he pointed out one of the “extras” in the book.  It turned out to be a classic, but very challenging, geometry puzzle.  It is interesting to see what it looks like when someone sees a puzzle like this for the first time.

Our discussion this morning was long, but really good (I hope!).  The four parts are below: