Three triangles ABC, CBD and ABD (where D is a point on AC) are all
isosceles. Find all the angles. Prove that the ratio of AB to BC is
equal to the golden ratio.
The diagram shows a regular pentagon with sides of unit length.
Find all the angles in the diagram. Prove that the quadrilateral
shown in red is a rhombus.
ABCDE is a regular pentagon of side length one unit. BC produced
meets ED produced at F. Show that triangle CDF is congruent to
triangle EDB. Find the length of BE.