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Year 9

Checking and securing understanding of similar triangles

I can recognise that similar shapes have sides in proportion to each other but angle sizes are preserved.

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New
New
Year 9

Checking and securing understanding of similar triangles

I can recognise that similar shapes have sides in proportion to each other but angle sizes are preserved.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. An enlargement means a change in size.
  2. The lengths of the lines may change when enlarged.
  3. The angles inside an object do not change when enlarged.
  4. When an object is enlarged, the image is similar.

Common misconception

You need to know all the lengths or all of the angles in a pair of triangles to know that they are similar.

Remind pupils that they do not necessarily need to know all of the length and angles to determine whether two triangles are congruent, so they don't all need to be known to determine similarity.

Keywords

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

  • Enlargement - Enlargement is a transformation that causes a change of size.

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

This lesson aims to recap prior learning about similar shapes while also preparing pupils to work with triangles inside a unit circle, later in this unit.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
What is the sum of internal angles of a triangle?
Correct Answer: 180
Q2.
Which of these is a property of an isosceles triangle?
All angles are always equal
Correct answer: Two angles are always equal
All sides are different lengths
Q3.
Which of these is a property of a right angled triangle?
Correct answer: $$a^2 + b^2 = c^2$$
All sides are equal in length
They cannot be isosceles.
Q4.
What are the sizes of the internal angles of a regular triangle?
Correct answer: 60ᵒ
50ᵒ
90ᵒ
Q5.
What type of triangle is this?
An image in a quiz
Correct answer: Scalene
Right angled
Equilateral
Isosceles
Q6.
Match the angle types
Correct Answer:Acute,< 90ᵒ

< 90ᵒ

Correct Answer:Right angle,90ᵒ

90ᵒ

Correct Answer:Obtuse,>90ᵒ and <180ᵒ

>90ᵒ and <180ᵒ

Correct Answer:Reflex,>180ᵒ

>180ᵒ

Correct Answer:Straight line,180ᵒ

180ᵒ

Exit quiz

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6 Questions

Q1.
Which of the following statements is true for these triangles?
An image in a quiz
Correct answer: The triangles are similar.
The triangles are not similar.
It is not possible to know whether the triangles are similar or not.
Q2.
For this pair of triangles, can you determine whether they are similar without using side lengths?
An image in a quiz
Correct answer: Yes, because their three angles correspond.
No because you only know two angles.
No, because you always need a side and two angles.
Q3.
Would a triangle ABC with sides AB = 8cm, BC = 6cm, AC = 10cm be similar to the one shown in the diagram?
An image in a quiz
Correct answer: Yes
No
Q4.
Which of these statements accurately describes mathematical similarity in shapes?
Their only difference is their angles. Their sides are in the same proportions.
Correct answer: 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.
Q5.
Which statement is true?
An image in a quiz
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.
Correct answer: A triangle with the same area as the one shown would not always be similar.
Q6.
What is the value of $$e$$?
An image in a quiz
Correct answer: 1
1.5
2
2.5