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.

Similarity in shapes

Maths

Checking understanding of similarity

Checking understanding of congruence

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

Which triangle is not similar to the others?

The table shows the base and height of four rectangles. Which rectangle is similar to a rectangle that is 2 cm by 5 cm?

∆ABC is similar to ∆ACD. The value of $$x$$ is {{ }}.

When an object is enlarged by a scale factor of 2, the object and its image are __________.

A triangle is enlarged by a scale factor of 2. Which of the following measurements will remain invariant?

Which angles are always equal when found on figure containing parallel lines and a transversal?

Which angle is corresponding with ∠ECD?

Which rectangle is not similar to rectangle R?

Triangle B is an enlargement of triangle A. What is the scale factor?

Similarity in shapes

Lesson outcome