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).

Demonstrating 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

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

What is the size of the largest angle in the triangle formed from these three squares?

Which of these three angles is the largest?

Which of these are possible sizes for the largest angle?

If three congruent squares are joined at their vertices, what type of triangle is formed?

Two congruent squares, A and B, and a third square, C, are joined at their vertices. The area of square C is less than the area of square A. What type of triangle is formed? 

It is impossible for a right-angled triangle to be made from these squares.

A right-angled triangle is formed from three squares. The area of two of the squares are 50 units² and 70 units². What are the possible areas of the third square?

The difference between 11² and 7² is {{}}.

Which of these show a fully and correctly correctly marked square?

angle around a point that makes one full turn

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

Demonstrating Pythagoras' theorem

Lesson outcome