The object is the starting figure before a transformation has been applied.

The image is the resulting figure after a transformation has been applied.

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

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

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

Checking understanding of similarity

Maths

Checking understanding of congruence

Similarity in shapes

Congruence in shapes

Congruent, similar or neither

Rotational symmetry

Congruent triangles (SSS)

Congruent triangles (SAS)

Congruent triangles (ASA and AAS)

Congruent triangles (RHS)

Applying the criteria for congruence

Demonstrating Pythagoras' theorem

Further demonstrating of Pythagoras' theorem

Length of the hypotenuse

Length of a shorter side

Determining which side

Pythagoras' theorem in context

Problem solving with similarity and Pythagoras' theorem

In this unit, pupils continued to build on their understanding of congruence and similarity with right-angled triangles. In the future unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

In the prior unit, pupils explored the effects of different transformations and whether the transformed shape was congruent or similar to the original shape. This is built on in this unit where pupils formalise the criteria for determining congruence in triangles and study rotational symmetry.

This unit explores the concepts of congruence and similarity, and ways to prove or disprove similarity between shapes. We then explore further properties of triangles with Pythagoras' Theorem.

Geometrical properties: similarity and Pythagoras' theorem

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

A shape is being enlarged by a scale factor of 4. One vertex is 3 cm from the centre of enlargement. Its corresponding vertex on the image will be {{}} cm from the centre of enlargement.

Sofia is enlarging the shape by a scale factor of 2. Which vertex has Sofia plotted incorrectly?

A parallelogram is enlarged by a scale factor of 3. Which of the following measurements will remain invariant?

The two triangles are similar. The value of $$x$$ is {{ }}.

A triangle has a base of 6 m and height of 2 m. A similar triangle, in the same orientation, has a base of 15 feet. Its height is {{}} feet.

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

The __________ is the multiplier between similar shapes that describes how large one shape is compared to the other.

Which rectangle is a correct enlargement of of rectangle R?

Triangle A has been enlarged by a scale factor of 2 to get triangle B. Match each unknown length from triangle B with its size.

A square has length 8 cm. It is enlarged by a scale factor of $$1\over{2}$$. The side length of its image is {{}} cm.

Each angle in an equilateral triangle is 60°. If an equilateral triangle is enlarged by a scale factor of 2, each of its angles will be {{}}°.

Checking understanding of similarity

Lesson outcome