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.

The amount of space occupied by a closed 3D shape.

Problem solving with advanced similarity knowledge

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

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

The multiplier between their corresponding edge lengths is $$k$$

The multiplier between their corresponding edge lengths is $$\frac {1}{2} k$$

The multiplier between their volumes is $$3k$$

The multiplier between their volumes is $$k^3$$

The multiplier between their volumes is $$\sqrt k$$

The multiplier between the surface areas of a pair of similar objects is $$k^2$$. Select the correct statements.

Shapes X and Y are similar to each other. The volume of shape Y is 216 times larger than the volume of shape X. The linear scale factor from X to Y is {{ }}.

Shapes X and Y are similar. The perimeter of shape Y is 125% of the perimeter of shape X. Work out the area scale factor from X to Y.

Pyramid A and pyramid B are similar. The surface area of pyramid A is 50 cm² and its volume is 120 cm³. The surface area of pyramid B is 450 cm². Calculate the volume of pyramid B.

Cuboid A and cuboid B are similar. The volume of cuboid B is 7680 cm³. The surface area of B is {{ }} cm².

{{}} theorem states that the sum 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 25 m. Select the possible lengths of the two shorter sides.

Which of these pairs of triangles are congruent? 

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.

Starter Quiz