A right-angled triangle has exactly one 90° interior angle.

A hypotenuse is the side of the right-angle triangle which is opposite the right-angle.

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).

Determining which side

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

Further demonstrating of Pythagoras' theorem

Length of the hypotenuse

Length of a shorter 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 these triangles are right-angled triangles?

impossible to tell, but this is a right-angled triangle

In the diagram, $$x$$ = 101, $$y$$ = 45, $$z$$ = 56.
Which of these angles is the right angle?

A right-angled triangle has sides of length 21 inches, 220 inches, and 221 inches.
Which of these are correct Pythagoras' theorem equations for this triangle?

A right-angled triangle has sides of length 39 inches, 80 inches, and 89 inches.
Which of these are correctly rearranged Pythagoras' theorem equations for this triangle?

Using Pythagoras' theorem, calculate the length of the side labelled $$j$$, rounded to 1 decimal place. Length of side $$j$$ is {{}} cm.

Using Pythagoras' theorem twice, calculate the length of the side labelled $$h$$, rounded to 2 decimal places. Length of side $$h$$ is {{}} cm.

In this diagram, $$a$$ cm² = 140 cm² and $$b$$ cm² = 185 cm².
The area $$c$$ cm² is {{}} cm².

In this diagram, $$b$$ cm² = 77 cm² and $$c$$ cm² = 107 cm².
Find the area $$a$$ cm².

In the diagram, $$a$$ = 1504 and $$b$$ = 1200.
Find the length of the hypotenuse of the triangle.

In this diagram, $$a$$ = 49, $$b$$ = 576, and $$c$$ = 625.
The perimeter of the triangle is {{}} cm.

In a right-angled triangle, one of its acute interior angles is 33°. What is the size of its other acute interior angle?

The size of an acute angle in a right-angled isosceles triangle is {{}}°.

Determining which side

Lesson outcome