So I need to show that the diagonal x satisfies the following ratio x/1=1/(x-1). I know this turns out to be the golden ratio, But I cant seem to find the similar triangles in order to find this ratio in this pentagon. Any help is appreciated, thanks
Let's label the vertices clockwise starting with the topmost vertex. Let's call them . Let's call the vertex in the center . Triangle ABE is similar to triangle CDF. You will want to show that BF=FE=1 and FC=FD=(x-1). Then .