The three triangles ABC, CBD and ABD are all isosceles. Find the angles in the triangles.

The sides AB and BC have lengths p and q respectively. Prove that the ratio p/q is equal to the golden ratio

${\displaystyle \frac{1}{2}(\sqrt{5}\hspace{1em}+1)}$

and find the ratio q/p.

The area of triangle ABC is 2 square units. Find the areas of CBD and ABD exactly (i.e. find the areas in the form

${\displaystyle a+b\sqrt{5}}$

where a and b are rational numbers)