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Year 9

Checking and securing understanding of Pythagoras' theorem

I can use Pythagoras' theorem to find the length of any side of a right-angled triangle.

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New
New
Year 9

Checking and securing understanding of Pythagoras' theorem

I can use Pythagoras' theorem to find the length of any side of a right-angled triangle.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. The sum of the squares of the two shorter sides equals the square of the longest side.
  2. The longest side is always opposite the right angle.
  3. a^2+b^2=c^2 can be rearranged to find one of the shorter side lengths.
  4. If the right-angled triangle is not immediately available, see if you can construct one.

Common misconception

Pupils may find it initially difficult to see how Pythagoras' theorem can be used when a right-angled triangle is not immediately available.

Encourage pupils to draw their own diagram in cases where there is not one provided. In cases where pairs of coordinates are being used, encourage pupils to draw on horizontal and vertical line segments.

Keywords

  • Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

  • 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.

To extend pupils further during the fourth learning cycle, they could be asked to think of other pairs of coordinates that would have the same distance from the origin as the points given in the examples and task.
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.
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.
Which of these statements is true?
Isosceles triangles are always similar to each other.
Correct answer: Equilateral triangles are always similar to each other.
Right triangles are always similar to each other.
Scalene triangles are always similar to each other.
Q3.
What is the value of n?
An image in a quiz
Correct Answer: 21, 21ᵒ
Q4.
Which of these statements is true?
Rectangles are always similar to each other.
Parallelograms are always similar to each other.
Rhombi are always similar to each other.
Correct answer: Squares are always similar to each other.
Q5.
What is the value of n?
An image in a quiz
Correct Answer: 158ᵒ, 158
Q6.
An isosceles triangle has an internal angle of 100ᵒ, what are the other two angles?
100ᵒ, 80ᵒ
Correct answer: 40ᵒ, 40ᵒ
60ᵒ, 60ᵒ

Exit quiz

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6 Questions

Q1.
In a right triangle, if the shortest sides are 6 cm and 8 cm, what is the length of the hypotenuse?
Correct answer: 10cm
12cm
8cm
Q2.
$$a^2+b^2=c^2$$ is a formula for which type of triangle?
scalene
isosceles
Correct answer: right angled
equilateral
Q3.
Which formula below is a rearrangement of $$a^2+b^2=c^2$$?
$$a^2+c^2=b^2$$
$$a^2-c^2=b^2$$
Correct answer: $$c^2-a^2=b^2$$
Q4.
In a right triangle, if the hypotenuse is 40 cm and a second side is 24 cm, what is the length of the third side? (Use a calculator to help you.)
Correct answer: 32 cm
30 cm
34 cm
Q5.
In a right triangle, if the hypotenuse is 30 cm and a second side is 24 cm, what is the area? (Use a calculator to help you.)
Correct answer: $$216 cm^2 $$
$$210 cm^2 $$
$$206 cm^2 $$
Q6.
In a right triangle, if the hypotenuse is 65 cm and a second side is 60 cm, what is the perimeter? (Use a calculator to help you.)
Correct answer: 150 cm
170 cm
140 cm