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Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

a right angled triangle drawn on a four-pin board

A right-angled triangle has been drawn on the four-pin board above left.

Can you draw the same type of triangle on a three-pin board?

How many pins could there be on the board for you to be able to draw the same type of triangle?

Do you notice anything about the number of pins for which this is possible?

What kind of triangle is drawn on the six-pin board above?

How many pins could there be on the board for you to be able to draw the same type of triangle?

Do you notice anything about the number of pins for which this is possible?

Can you name the type of triangle drawn on the nine-pin board above?

On what size board could you draw the same type of triangle?

Do you notice anything about the number of pins for which this is possible?

You might 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 mm in diameter), together with a teacher's guide, are available from Geoff at Education Initiatives
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.