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

Congruent triangles (SSS)

Maths

Checking understanding of similarity

Checking understanding of congruence

Similarity in shapes

Congruence in shapes

Congruent, similar or neither

Rotational symmetry

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

If triangle ABC is congruent to triangle PQR. Match the corresponding equal edges.

Triangle MNO is congruent to triangle ABC by SSS and MN is 11 cm. Which angle in triangle MNO is opposite MN?

Yes - their corresponding angles are the same.

No - the corresponding edges are not the same.

Triangle MNO has two angles of 103° and 32°. Side MN is 12 cm. Are triangle ABC and MNO congruent?

as ST and SV are both edges of the same square.

as TU and VU are both edges of the same square.

STUV is a square. Match each statement to a reason to prove that triangle STU is congruent to triangle SVU by SSS.

Jun measures each of these triangles. Which of the triangles are congruent to this triangle by SSS?

PQRS is an isosceles trapezium. PR = QS. Match the letters in the proof with the correct edge.

In degrees, what is the size of the angle shown?

Select all the quadrilaterals that have at least one pair of equal sides.

These two rectangles are similar. This means that the side marked $$x$$ is {{ }} cm.

Quadrilaterals ABCD and HEFG are congruent. Match each side or angle in quadrilateral ABCD with a corresponding edge or angle in quadrilateral HEFG.

A transformation has taken place on a shape. The image is congruent to the object. Which transformation cannot have taken place?

Match each quadrilateral with another quadrilateral that could have the same interior angles.

Starter Quiz

In degrees, what is the size of the angle shown?