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Broad Topics > 2D Geometry, Shape and Space > Similar triangles

Pythagoras Proofs

Stage: 4 Challenge Level:

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

Partly Circles

Stage: 4 Challenge Level:

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

Matching Triangles

Stage: 1 Challenge Level:

Can you sort these triangles into three different families and explain how you did it?

Stage: 5 Challenge Level:

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

The Line and Its Strange Pair

Stage: 4 Challenge Level:

In the diagram the point P' can move to different places along the dotted line. Each position P' takes will fix a corresponding position for P. If P' moves along a straight line what does P do ?

Trapezium Four

Stage: 4 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?

Triangle Midpoints

Stage: 4 Challenge Level:

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

Kite in a Square

Stage: 4 Challenge Level:

Can you make sense of the three methods to work out the area of the kite in the square?

Pinhole Camera

Stage: 3 Challenge Level:

Make your own pinhole camera for safe observation of the sun, and find out how it works.

Stage: 4 and 5 Challenge Level:

How would you design the tiering of seats in a stadium so that all spectators have a good view?

It Depends on Your Point of View!

Stage: 4 Challenge Level:

Anamorphic art is used to create intriguing illusions - can you work out how it is done?

Number the Sides

Stage: 2 Challenge Level:

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

Mapping the Wandering Circle

Stage: 4 Challenge Level:

In the diagram the point P can move to different places around the dotted circle. Each position P takes will fix a corresponding position for P'. As P moves around on that circle what will P' do?

Points in Pairs

Stage: 4 Challenge Level:

In the diagram the radius length is 10 units, OP is 8 units and OQ is 6 units. If the distance PQ is 5 units what is the distance P'Q' ?

Look Before You Leap

Stage: 4 Challenge Level:

The diagonals of a square meet at O. The bisector of angle OAB meets BO and BC at N and P respectively. The length of NO is 24. How long is PC?

Double Angle Triples

Stage: 5 Challenge Level:

Try out this geometry problem involving trigonometry and number theory