Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?
What fractions can you divide the diagonal of a square into by simple folding?
Drawing a triangle is not always as easy as you might think!
Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.
Explain how to construct a regular pentagon accurately using a straight edge and compass.
Investigate constructible images which contain rational areas.
