Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.

Enlargement is a transformation that causes a change of size.

Scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

Checking and securing understanding of similar triangles

Maths

Checking and securing understanding of Pythagoras' theorem

The unit circle

Scaling the right-angled triangle from the unit circle

Sine and cosine ratios

Tangent ratio

Using the sine ratio

Using the cosine ratio

Using the tangent ratio

Choosing the right trigonometric ratio

Choosing an appropriate method for finding lengths of a triangle

Problem solving with trigonometry

In this unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In the future unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

In the prior unit, pupils continued to build on their understanding of congruence and similarity with right-angled triangles. In this unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

In this unit pupils learn how to recognise the relationship between the unit circle and the trigonometric ratios of sine, cosine and tangent. Pupils then apply this knowledge to solve trigonometric problems.

Trigonometry

It is not possible to know whether the triangles are similar or not.

Which of the following statements is true for these triangles?

Yes, because their three angles correspond.

No, because you always need a side and two angles.

For this pair of triangles, can you determine whether they are similar without using side lengths?

Would a triangle ABC with sides AB = 8cm, BC = 6cm, AC = 10cm be similar to the one shown in the diagram?

Their only difference is their angles. Their sides are in the same proportions.

Their only difference is their size. Their sides are in the same proportions.

Their only difference is their sides. Their area is exactly the same.

Which of these statements accurately describes mathematical similarity in shapes?

A triangle with the same perimeter as the one shown would always be similar.

A triangle with the same area as the one shown would always be similar.

A triangle with the same area as the one shown would not always be similar.

What is the sum of internal angles of a triangle? 

Which of these is a property of an isosceles triangle?

Which of these is a property of a right angled triangle?

What are the sizes of the internal angles of a regular triangle?

Checking and securing understanding of similar triangles

Lesson outcome