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

Congruent triangles (SAS)

Maths

Checking understanding of similarity

Checking understanding of congruence

Similarity in shapes

Congruence in shapes

Congruent, similar or neither

Rotational symmetry

Congruent triangles (SSS)

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

When there are two triangles, if the two corresponding edges and the angle between them are the same, you can prove they are congruent by {{ }} (side-angle-side).

If triangles ABC and XYZ are congruent by SAS then {{ }} is 9.6 cm.

Which of the following triangles have sufficient information to guarantee they are congruent to triangle ABC?

Which of the following triangles are congruent to triangle XYZ?

Yes, they are guaranteed to be congruent.

as they are interior angles of a regular hexagon (= 120°)

as they are interior angles of a square (= 90°)

as they are in regular polygons with shared edges

This diagram shows a regular hexagon ABCDEF and a square AGHF. Match the statements to prove triangle ABG and FHE are congruent by SAS.

The two marked angles are __________ angles in parallel lines.

four sets of supplementary co-interior angles

Select all the properties of a parallelogram.

Rectangle A and rectangle B are similar. The length of the side marked $$x$$ is {{ }}cm.

Triangle ABC and triangle XYZ are congruent. Which edge is 6.5 cm on triangle XYZ?

The diagram shows two pairs of lines intersecting at a point. The value of $$x$$ is {{ }}.

Congruent triangles (SAS)

Lesson outcome