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How many triangles can you make on the 3 by 3 pegboard?

Cutting Corners

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?


Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Putting Two and Two Together

Age 7 to 11
Challenge Level

Two equilateral triangles can be put together in one way only, if they must touch all along a side:


two equilateral triangles


These isosceles triangles of the same area can be put together in more than one way.

Remember that reflection can be used as well as rotation when finding the ways.




two isosceles triangles


Can you find any other ways?

You could cut out triangles from these sheets.

These triangles are half of the above equilateral and isosceles triangles:




two smaller triangles


In how many ways do you think two of these can be put together using, reflection as well as rotation, if same-sized sides must touch the full length of the side?

Can you give any reasons for this?

You could cut some of your other triangles in half to test out your prediction.

Can you find a triangle such that two identical copies of it can be put together in more ways keeping to the rule that same-sized sides must touch the full length of the side?