Pentagon Construction

To show that the construction yields a regular pentagon, you might find it useful to use cartesian coordinates. Take A to be (0,0) and B to be (1,0). Can you work out the coordinates of the other points?

Can you use Pythagoras to work out any of the lengths in your diagram?

How might the identities for $\cos 72^{\circ}$ and $\cos 144^{\circ}$ help?