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

Applying the criteria for congruence

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 (ASA and AAS)

Congruent triangles (RHS)

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 of the following are criteria for proving two triangles are congruent?

Triangle ABC and triangle DEF are congruent by __________.

There is insufficient information to prove triangle ABC is congruent to triangle MNO by __________.

Triangle KLM is __________ to triangle XYZ.

If you know that ABCD is a parallelogram, then __________ criteria for congruent triangles (ASA, RHS, SAS and SSS) can be used to show ABD and BDC are congruent.

Matching a, b, c and d to the correct statements to complete this congruence proof.

Select the right-angled triangles. (Diagrams are not drawn accurately)

The square has a perimeter of 36 cm. The perimeter of the regular hexagon is {{ }}cm.

All of these triangles are translations, rotations or reflections of each other. If they were cut out you could fit them exactly on of top of each other. You can say the triangles are {{ }}.

The quadrilaterals ABCD and EFGH are congruent and AD = 6 cm. Which edge on EFGH is also 6 cm?

congruent as the three interior angles are all the same.

similar as the three interior angles are the same.

Complete the statement. Triangle ABC and triangle XYZ are ____________.

Applying the criteria for congruence

Lesson outcome