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Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

Two by One

An activity making various patterns with 2 x 1 rectangular tiles.

Tetrafit

Age 7 to 11 Challenge Level:
This sheet may be useful if you can't use the interactivity.
Remember you can turn the pieces round.
Will you need to fill the whole board?