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

Co-interior angles are on the same side of the transversal line and in between the two other lines.

Congruence in shapes

Maths

Checking understanding of similarity

Checking understanding of congruence

Similarity 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

Triangles A and B are congruent. Match each unknown length from triangle B with its size.

Triangles A and B are congruent. Match each unknown angle from triangle B with its size.

The image shows two congruent hexagons. What is the size of the angle $$x°$$?

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

Shape T is a trapezium. Which quadrilateral contains enough information to determine whether it is congruent to shape T?

Shape R is a rhombus. Which quadrilateral is not congruent to shape R?

Which transformations always produce an image that is congruent to the object?

When two shapes are congruent, which property of the shapes always remain invariant?

The table shows the base and height of four rectangles. Which rectangle is congruent to a rectangle that is 6 cm by 3 cm?

Which triangle is congruent to triangle T?

The diagram shows a pair of angles on parallel lines. When $$x=145$$, $$y=$${{}}.

Congruence in shapes

Lesson outcome