Pythagoras' theorem

There are 108 NRICH Mathematical resources connected to Pythagoras' theorem

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Favourite

Pythagoras proofs

Age

11 to 16

Challenge level

Can you make sense of these three proofs of Pythagoras' Theorem?

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Garden shed

Age

11 to 14

Challenge level

Can you minimise the amount of wood needed to build the roof of my garden shed?

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Favourite

Kite in a square

Age

14 to 18

Challenge level

Can you make sense of the three methods to work out what fraction of the total area is shaded?

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Favourite

Generating triples

Age

14 to 16

Challenge level

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

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Favourite

Zig zag

Age

14 to 16

Challenge level

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?

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Favourite

Orthogonal circle

Age

16 to 18

Challenge level

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

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Favourite

Partly circles

Age

14 to 16

Challenge level

What is the same and what is different about these circle questions? What connections can you make?

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Favourite

Three cubes

Age

14 to 16

Challenge level

Can you work out the dimensions of the three cubes?

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Favourite

Hex

Age

11 to 14

Challenge level

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

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Favourite

In a right-angled tetrahedron prove that the sum of the squares of the areas of the 3 faces in mutually perpendicular planes equals the square of the area of the sloping face. A generalisation of Pythagoras' Theorem.

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For younger learners

Pythagoras' theorem

Pythagoras proofs

Garden shed

Kite in a square

Generating triples

Zig zag

Orthogonal circle

Partly circles

Three cubes

Hex

Pythagoras for a tetrahedron