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

1 2 (Ö5 +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

a + b Ö5

where a and b are rational numbers)