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'Triangle Pin-down' printed from http://nrich.maths.org/

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Have you looked at the angles in the triangles drawn? It might help to draw in some radii and work out angles from the centre.

How will you record the triangles you can make? You might like to print off these sheets if you're not using the interactivity:
Sheet of three-peg boards
Sheet of four-peg boards
Sheet of five-peg boards
Sheet of six-peg boards
Sheet of seven-peg boards
Sheet of eight-peg boards
Sheet of nine-peg boards