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### There are 16 results

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:

Can you spot a cunning way to work out the missing length?

### Double Angle Triples

##### Stage: 5 Challenge Level:

Try out this geometry problem involving trigonometry and number theory