Pythagoras’ theorem shows that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of its longest side (the hypotenuse).

Further demonstrating of Pythagoras' theorem

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)

Applying the criteria for congruence

Demonstrating 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

What is the missing side length of a right-angled triangle with legs of size 3 and 4 units?

What is the missing side length of a right-angled triangle with legs of size 6 and 8 units?

What is the missing side length of a right-angled triangle with hypotenuse 13 units, and a shorter side of length 5 units?

What is the area of a right angled triangle with hypotenuse of length 25 units, and base of length 7 units?

The lengths of sides of different triangles are provided below. Which ones are right angled triangles?

What is the size of the hypotenuse for a right-angled isosceles triangle with legs of 4 units?

The difference between 10² and 6² is {{}}.

Starting with the smallest, place these angles in order of size.

Which two of these are not square numbers?

Further demonstrating of Pythagoras' theorem

Lesson outcome