Triangles All Around

Triangles All Around


You might like to have a look at Nine-Pin Triangles before trying this problem.

How many different triangles can you draw on a circular pegboard which has four equally spaced pegs?

What are the angles of each triangle?

If you have a six-peg circular pegboard, how many different triangles are possible now?

What are their angles?

How many different triangles could you draw on an eight-peg board?
Can you find the angles of each?

You may like to use the interactivity to try out your ideas.
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For printable sets of circle templates for use with this activity, please see Printable Resources page.

Many thanks to Geoff Faux who introduced us to the merits of the 9 pin circular geo-board.

The boards, moulded in crystal clear ABS that can be used on an OHP (185 cm in diameter), together with a teacher's guide, are available from Geoff at Education Initiatives

This problem offers an opportunity for pupils to work in a systematic way, using their knowledge of the properties of triangles. A useful discussion about which triangles are the same and which are different could be encouraged.

Students will need to apply what they know about angles in circles and triangles in order to calculate the angles in each triangle they draw. The problem encourages them to be clear about what they do know and what they can work out from it.

If working on paper rather than using the interactivity, pupils may find it helpful to print these sheets off:

Sheet of four-peg boards
Sheet of six-peg boards
Sheet of eight-peg boards