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

Checking understanding of congruence

Maths

Checking understanding of similarity

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

Which transformation can produce an image that is incongruent to an object?

Which triangles are congruent to triangle T?

Shapes A and B are congruent. Match each unknown length from shape B with its size.

When two shapes are congruent, which property of the shapes may differ?

The type of transformation that maps shape A onto shape B is a {{ }}.

changing the size of an object while maintaining the same proportions

turning an object by a fixed amount and around a fixed point

moving every point of an object by the same distance and direction

Match each transformation to its description.

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

Which properties of a triangle would remain invariant when it is rotated 90°.

A square with length 5 cm is enlarged by a scale factor of 1. The length of square in the image is {{}} cm.

Which of the triangles can NOT be obtained by reflecting triangle T?

Triangle A has been reflected over the line of reflection to create triangle B. Match each unknown length from triangle B with its size.

Starter Quiz

Match each transformation to its description.