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

Congruent triangles (ASA and AAS)

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 (SAS)

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

True - if you know two angles in a triangle then you can calculate the third.

False - one is where you know the side between two angles and the other isn't.

The criteria ASA (angle-side-angle) and AAS (angle-angle-side) are equivalent. True or false?

Triangle ABC and triangle XYZ are congruent by AAS/ASA. Which angle in triangle XYZ is 46°?

Match each triangle on the top row to the triangle on the bottom row that it is congruent to.

Which of the following triangles is not guaranteed to be congruent to the other three triangles?

Which of these quadrilaterals can be split into two congruent triangles using one diagonal?

Complete this congruence proof. ∠ABD = ∠BDC as they are given in the diagram, BD is a shared edge and ∠ADB = ∠DBC as they are equal {{ }} angles, so triangle ABD and BDC are congruent by SAS.

Which line segment has not been drawn to the same length as the other two?

The missing angle in triangle XYZ is {{ }}°.

Triangle ABC is congruent to triangle XYZ, therefore YZ = {{ }} cm.

Triangle ABC and triangle XYZ are congruent, therefore {{ }} is 9.6 cm.

Congruent triangles (ASA and AAS)

Lesson outcome