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Sorting Symmetries

Age 7 to 11 Challenge Level:

Naomi has a triangle which is blue on one side and yellow on the other. It has a dot in one corner on each side.
How many ways are there of posting this triangle through a triangular shaped slot? (You may like to use the interactivity from our Turning Triangle problem to help you.)

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All these ways of posting the triangle are different. They can be called symmetries of the triangle. Can you work out a way to describe each one? You might like to choose a symbol for each.

Naomi finds that she can turn the triangle and then flip the triangle vertically so that she gets another symmetry. What might the triangle have looked like before she flipped it vertically, and what might it look like afterwards?