Skip to content
Oak National Academy
Oak National Academy
Teachers
Pupils
New
New
Year 9

Problem solving with similarity and Pythagoras' theorem

I can use my knowledge of similarity and Pythagoras' theorem to solve problems.

Download all resources
arrow-right
Share activities with pupils
arrow-right
New
New
Year 9

Problem solving with similarity and Pythagoras' theorem

I can use my knowledge of similarity and Pythagoras' theorem to solve problems.

Download all resources
arrow-right
Share activities with pupils
arrow-right
warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.
View new resources
arrow-right

Lesson details

Key learning points

  1. Right-angled triangles can be seen in real-life (e.g. ladder against a vertical wall).
  2. A ratio table can help you find the scalar and functional multipliers in similar shapes.
  3. It can be initially difficult to identify whether Pythagoras' theorem can be used.

Keywords

  • Pythagoras’ theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.

Common misconception

Every question that has a right-angled triangle must use Pythagoras' theorem to be solved.

It is easy to get into a habit of using Pythagoras' theorem when learning the topic, but it is likely you have seen several maths problems in the past with right-angled triangles, which ask to find areas and angles, without using Pythagoras' theorem.

If two right-angled triangles are similar, then the length of a side of one triangle calculated using Pythagoras theorem will have the same multiplicative scale factor applied as any other side of that triangle.
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).

Lesson video

Skip lesson video

Loading...

Starter quiz

Download starter quiz

6 Questions

Q1.
Alex rearranges a correct Pythagoras' theorem equation for a triangle. Which of these statements are correct?
An image in a quiz
Correct answer: The hypotenuse of the triangle is side P
The hypotenuse of the triangle is side Q
The hypotenuse of the triangle is side R
Correct answer: Side R has length of 60 units.
Side R has length of 69.64 units.
Q2.
The perimeter of this right-angled triangle is cm.
An image in a quiz
Correct Answer: 182, 182 cm, 182cm
Q3.
Adhesive tape is placed along the two diagonals of this rectangular picture frame. How much adhesive tape is needed, rounded to the nearest cm? cm of tape.
An image in a quiz
Correct Answer: 186, 186 cm, 186cm
Q4.
Andeep and Sofia need to split a 3.6 metre roll of adhesive tape in the ratio 7 : 5. The length of the adhesive tape that Andeep receives is centimetres.
Correct Answer: 210, 210 cm, 210cm
Q5.
These two triangles are similar to each other. The side marked $$u$$ cm is cm long.
An image in a quiz
Correct Answer: 64, 64 cm, 64cm
Q6.
An isosceles triangle has an angle of 22°. Which of these are possible sizes of one of the other angles?
11°
Correct answer: 22°
45°
Correct answer: 79°
Correct answer: 136°

Exit quiz

Download exit quiz

6 Questions

Q1.
These two triangles are similar to each other and are both in the same orientation. The length of the hypotenuse marked $$h$$ is cm.
An image in a quiz
Correct Answer: 40, 40 cm, 40cm
Q2.
The area of this triangle is cm².
An image in a quiz
Correct Answer: 120, 120 cm², 120cm², 120 cm squared, 120cm squared
Q3.
Which of these statements are correct for this triangle?
An image in a quiz
You need to use Pythagoras' theorem to find the size of angle $$g$$.
Correct answer: You do not need to use Pythagoras' theorem to find the size of angle $$g$$.
$$g$$° = 27°
Correct answer: $$g$$° = 43°
$$g$$° = 47°
Q4.
Which of these statements are correct for this triangle?
An image in a quiz
Correct answer: The perimeter of this triangle is 16 + 25.4 + 19.7 = 61.1 cm (to 1 d.p.).
The perimeter of this triangle is 16 + 25.4 + 25.4 = 92.4 cm (to 1 d.p.).
Correct answer: The area of this triangle is 158 cm² (to the nearest cm²).
The area of this triangle is 203.2 cm² (to 1 d.p.).
$$f°$$ = 180° − 90° − 51° = 39°.
Q5.
Each square is 1 unit in length. The shortest distance from point A to point B is units (rounded to 2 d.p.).
An image in a quiz
Correct Answer: 10.05, 10.05 units, 10.05units
Q6.
Point C is at the coordinate (12, 3). The perimeter of a triangle whose vertices are at points A, B, and C is units (to the nearest unit).
An image in a quiz
Correct Answer: 32, 32 units, 32units