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Putting Two and Two Together

Age 7 to 11 Challenge Level:

Caroline from St Jude's C of E School said that she found one more way to put the green (isosceles) triangles together. She sent this picture of all three ways:

ways to put two isosceles together

Sally says thereis one more way than this, as because we are not allowing reflection of the triangles themselves, then we could make the longer shape again, but the other way round, so the down pointing triangle was to the right of the up pointing triangle.

Caroline then goes on to suggest:

The half equilateral and isosceles triangles can be joined in three ways, because the triangles have three different length sides.

Francesca noticed:

The two blue triangles are the same, just reflected of each other. They are scalene because all their angles and sides are different lengths. They are also Right Angled Triangles.

So if there are three different edge lengths, and then also two ways of rotating the other triangle to place it there are 6 ways like in my picture.

Great! Why not now explore putting the yellow, blue and green triangles all together. Watch out for different edge lengths!

If anyone has any further ideas, please do get in touch with us.