Pythagoras' theorem

There are 108 NRICH Mathematical resources connected to Pythagoras' theorem

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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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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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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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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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Where to land

Age

14 to 16

Challenge level

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

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Favourite

Cubestick

Age

16 to 18

Challenge level

Stick some cubes together to make a cuboid. Find two of the angles by as many different methods as you can devise.

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Belt

Age

16 to 18

Challenge level

A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.

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For younger learners

Pythagoras' theorem

Pythagoras proofs

Garden shed

Kite in a square

Generating triples

Three cubes

Hex

Pythagoras for a tetrahedron

Where to land

Cubestick

Belt