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

If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

Congruent, similar or neither

Maths

Checking understanding of similarity

Checking understanding of congruence

Similarity in shapes

Congruence in shapes

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

The two shapes in the image are __________.

Which triangle is congruent to triangle T?

Which triangle is similar to triangle T, but not congruent to triangle T?

Rectangle A has lengths 3 cm by 6 cm. Rectangle B is congruent to rectangle A. One of the lengths of rectangle B is 6 cm, so the other length is {{}} cm.

The image shows two congruent pentagons. What is the value of $$x$$?

The image shows two similar hexagons. The size of the angle $$x°$$ is {{ }}°.

Rectangle A has lengths 3 cm by 6 cm. Rectangle B is similar, but not congruent, to rectangle A. One of the lengths of rectangle B is 6 cm, so the other length is {{}} cm.

Congruent, similar or neither

Lesson outcome