Two shapes are similar if the only difference between                        them is their size. Their side lengths are in the same proportions.

A property of a shape is invariant if that property has not changed after the shape is transformed.

Enlargement is a transformation that causes a change of size.

A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

Problem solving with similarity

Maths

In the prior unit, pupils enhanced their understanding of enlargement. In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.

Similarity

Similarity can be used in architecture or in mechanical drawings to make a {{}} drawing of a real world object.

This is a scale drawing of a van. The height of the van is {{ }} metres.

This is a scale drawing of a van. The length of the van is {{ }} metres.

Sam is wrong, you can't have a decimal scale factor

The object and image aren’t similar because Sam enlarged it incorrectly.

The object and image aren't similar as the angles are not invariant

Object and image are similar as all enlargements are similar to their object.

The object and image are similar as the angles are invariant

Sam has attempted to enlarge this object by a scale factor of 2.5. Which statements are correct?

The dashed triangle shows the route a bird took between its nest N, a lake L and an old manor house M. The bird flies direct from its nest to the manor and then to the lake. How far does it fly?

The dashed triangle shows the route a bird took between its nest N, a lake L and an old manor house M. The bird flies direct from its nest, N, to the lake, L. The distance the bird flies is {{ }} km.

Which of these pairs of triangles are congruent? 

Pythagoras’ theorem states that the {{}} of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

The lengths of the 3 edges of some triangles are given. Select all the right-angled triangles.

A right-angled triangle has a hypotenuse of 65 mm. Select the possible lengths of the two shorter sides.

Triangle ABC and triangle DEF are congruent and AB > BC. The length of the side $$x$$ is {{}} cm.

Match each letter which the correct statement to complete the proof that triangle DAC and triangle ABC are congruent.

This lesson will be removed by end of Summer Term 2025.

Problem solving with similarity

Lesson outcome

This lesson will be removed by end of Summer Term 2025.