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.

Using the scale factor for enlarging an area

Maths

Checking and securing understanding of direct proportion in context

The effect of enlargement on the perimeter of a shape

The effect of enlargement on the area of a shape

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

The transformation that causes a change in size of the object is {{}}.

Rectangles A and B are similar. What is the area scale factor from A to B?

Shapes P and Q are similar. The perimeter of shape P is 20 cm and the perimeter of shape Q is 40 cm. The area scale factor from P to Q is {{}}.

Sectors E and F are similar. The area of sector E is 25π cm². What is the area of sector F?

Sectors E and F are similar. The area of shape E is 26π cm² and the area of sector F is 58.5π cm². The radius of sector F is {{}} cm.

Triangles L and M are similar. The area of triangle M is 150 cm². What is the perimeter of triangle M?

A hexagon is enlarged by scale factor 3. What properties of the hexagon and its image are invariant? 

The perimeter of rectangle A is $$\frac{1}{9} $$ the perimeter of rectangle B

The perimeter of rectangle A is $$\frac{1}{3}$$ the perimeter of rectangle B

The area of rectangle A is $$\frac{1}{3}$$t he area of rectangle B

The area of rectangle A is $$\frac{1}{9}$$ the area of rectangle B

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

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 24 cm². The area of shape S is {{ }} cm².

Using the scale factor for enlarging an area

Lesson outcome