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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 or you might want to use the interactivity below:

Full Screen Version

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?

Full Screen Version

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?