# Math Help - Golden ratio pentagon

1. ## Golden ratio pentagon

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

2. ## Re: Golden ratio pentagon

Let's label the vertices clockwise starting with the topmost vertex. Let's call them $A,B,C,D,E$. Let's call the vertex in the center $F$. Triangle ABE is similar to triangle CDF. You will want to show that BF=FE=1 and FC=FD=(x-1). Then $\dfrac{1}{x-1} = \dfrac{EA}{FD} = \dfrac{BE}{CD} = \dfrac{x}{1}$.

3. ## Re: Golden ratio pentagon

I suggest reading this article I wrote (it's also in the MHF Magazine, Issue 2 I think) from page 10.