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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


Why do this problem?

This problem offers an opportunity for pupils to work in a systematic way, using their knowledge of the properties of triangles.  Learners 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.

Possible approach

It would be a good idea to try Nine-pin Triangles before tackling this task.  You may like to read the teachers' notes of that task and follow a similar approach.  A useful discussion about which triangles are the same and which are different could be encouraged.

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

Key questions

How do you know your triangles are all different?
How do you know you have got all the different triangles?
What do you know about the angles in a circle?
What do you know about the angles in a triangle?

Possible support

Working in pairs will help learners access this task.  After some time, you could encourage two pairs to join forces and compare their ways of working.