Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Checking and securing understanding of Pythagoras' theorem

      Lesson details

      Learning outcome

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

      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.

      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.

      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.

      Teacher tip

      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.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      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

      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

      To help you plan your 9 maths lesson on: Checking and securing understanding of Pythagoras' theorem, download all teaching resources for free and adapt to suit your pupils' needs...