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 effect of enlargement on the area of a shape

Maths

Checking and securing understanding of direct proportion in context

The effect of enlargement on the perimeter of a shape

Using the scale factor for enlarging an area

The effect of enlargement on the volume of a 3D shape

Using the scale factor for enlarging a volume

Checking and securing understanding of congruent triangles (SSS)

Checking and securing understanding of congruent triangles (SAS)

Checking and securing understanding of congruent triangles (ASA)

Checking and securing understanding of congruent triangles (RHS)

Problem solving with advanced similarity knowledge

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.

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

A pentagon is enlarged by scale factor 2. What properties of the pentagon and its image are invariant? 

The perimeter of rectangle B is 3 × the perimeter of rectangle A

The perimeter of rectangle B is 9 × the perimeter of rectangle A

The area of rectangle B is 3 × the area of rectangle A

The area of rectangle B is 6 × the area of rectangle A

The area of rectangle B is 9 × the area of rectangle A

Rectangle A has been enlarged to create rectangle B. Select the correct statements.

Rectangle A has been enlarged to create rectangle B. The area of rectangle B is {{ }} cm²

Trapezium B is an enlargement of trapezium A. Calculate the area of trapezium B.

Match each linear scale factor to the area scale factor.

Shape S is an enlargement an enlargement of shape R. The area of shape R is 32 cm². The area of shape S is {{ }} cm².

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

This sector is enlarged by scale factor $$\frac{1}{2}$$. The angle in the image is {{}}°.

Each square on this coordinate grid is 1 unit long. This object is enlarged by a scale factor of 4 to make its image. Calculate the perimeter of the image.

A pentagon has a perimeter of 60 cm. The pentagon is enlarged by scale factor 7. The perimeter of the image is {{}} cm.

The object is enlarged by a scale factor of $$\frac{1}{3}$$ to make the image. What is the perimeter of the image?

A shape is enlarged by a scale factor of $$\frac{3}{2}$$ to make its image. The perimeter of the image is 42 cm. The perimeter of the object is {{ }} cm.

Exit Quiz

A pentagon is enlarged by scale factor 2. What properties of the pentagon and its image are invariant?