New
New
Year 9
Problem solving with similarity and Pythagoras' theorem
I can use my knowledge of similarity and Pythagoras' theorem to solve problems.
New
New
Year 9
Problem solving with similarity and Pythagoras' theorem
I can use my knowledge of similarity and Pythagoras' theorem to solve problems.
Lesson details
Key learning points
- Right-angled triangles can be seen in real-life (e.g. ladder against a vertical wall).
- A ratio table can help you find the scalar and functional multipliers in similar shapes.
- It can be initially difficult to identify whether Pythagoras' theorem can be used.
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.
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.
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).
Video
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Starter quiz
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6 Questions
Q1.
Alex rearranges a correct Pythagoras' theorem equation for a triangle. Which of these statements are correct?
Correct answer: The hypotenuse of the triangle is side P
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 60 units.
Side R has length of 69.64 units.
Q2.
The perimeter of this right-angled triangle is cm.
Correct Answer: 182, 182 cm, 182cm
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.
Correct Answer: 186, 186 cm, 186cm
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
210, 210 cm, 210cm
Q5.
These two triangles are similar to each other. The side marked $$u$$ cm is cm long.
Correct Answer: 64, 64 cm, 64cm
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°
22°
45°
Correct answer: 79°
79°
Correct answer: 136°
136°
Exit quiz
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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.
Correct Answer: 40, 40 cm, 40cm
40, 40 cm, 40cm
Q2.
The area of this triangle is cm².
Correct Answer: 120, 120 cm², 120cm², 120 cm squared, 120cm squared
120, 120 cm², 120cm², 120 cm squared, 120cm squared
Q3.
Which of these statements are correct for this triangle?
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 $$g$$.
You do not need to use Pythagoras' theorem to find the size of angle $$g$$.
$$g$$° = 27°
Correct answer: $$g$$° = 43°
$$g$$° = 43°
$$g$$° = 47°
Q4.
Which of these statements are correct for this triangle?
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 + 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 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.).
Correct Answer: 10.05, 10.05 units, 10.05units
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).
Correct Answer: 32, 32 units, 32units
32, 32 units, 32units