Similarity and congruence

There are 62 NRICH Mathematical resources connected to Similarity and congruence

problem

Favourite

Pythagoras proofs

Age

11 to 16

Challenge level

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

problem

Favourite

Triangle in a trapezium

Age

11 to 16

Challenge level

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

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Favourite

The square under the hypotenuse

Age

14 to 16

Challenge level

Can you work out the side length of a square that just touches the hypotenuse of a right angled triangle?

problem

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?

problem

Favourite

Triangle midpoints

Age

14 to 16

Challenge level

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

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Favourite

Trapezium four

Age

14 to 16

Challenge level

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

problem

Favourite

Two ladders

Age

14 to 16

Challenge level

Two ladders are propped up against facing walls. At what height do the ladders cross?

problem

Favourite

All about ratios

Age

16 to 18

Challenge level

A new problem posed by Lyndon Baker who has devised many NRICH problems over the years.

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Favourite

Nicely similar

Age

14 to 16

Challenge level

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

problem

Favourite

Sitting pretty

Age

14 to 16

Challenge level

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

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Similarity and congruence

Pythagoras proofs

Triangle in a trapezium

The square under the hypotenuse

Kite in a square

Triangle midpoints

Trapezium four

Two ladders

All about ratios

Nicely similar

Sitting pretty