How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

The length AM can be calculated using trigonometry in two different ways. Create this pair of equivalent calculations for different peg boards, notice a general result, and account for it.

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?

Suggestions for worthwhile mathematical activity on the subject of angle measurement for all pupils.

A virtual geoboard that allows you to create shapes by stretching rubber bands between pegs on the board. Allows a variable number of pegs and variable grid geometry and includes a point labeller.

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?