The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

Congruent triangles (RHS)

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)

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

The hypotenuse is the side of a right-angle triangle which is {{ }} the right angle.

Which side in this triangle is the hypotenuse?

Triangle ABC and JKL are congruent by __________.

Which of the these triangles are congruent to triangle ABC?

given on the diagram. PQR is an isosceles triangle.

given on the diagram. PS is the altitude of the triangle.

is a common edge to both triangles PQS and PRS

Match each statement to a correct justification to prove that triangle PQS is congruent to triangle PRS by RHS.

Yes - they both share a side, they both have a right angle and one side is 2 cm

No - the hypotenuse of one is a short side of another

Not enough information - you do not know the other angles in the triangle

Can triangles ABD and BCD ever be congruent?

Convert this measurement to centimetres: 23 mm = {{ }} cm.

Which of these triangles can contain a right angle?

In all right-angled triangles, what is true about the angles $$a°$$ and $$b°$$?

In this right-angled triangle, $$a°=$${{ }}°

Starter Quiz

Convert this measurement to centimetres: 23 mm = cm.