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      Checking and further securing understanding of Pythagoras' theorem

      Lesson details

      Learning outcome

      I can use Pythagoras' theorem to calculate the length of a 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. The difference between the squares of the longest and known shorter sides is the square of the remaining side
      4. A calculator can perform these calculations efficiently
      5. Rounding gives a less accurate answer so there might be times you wish to leave your answer with an operator

      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

      Misidentifying the hypotenuse.

      The hypotenuse is the longest side of a right-angled triangle. It is always opposite the right-angle.

      Teacher tip

      In Task C Q1h, you may wish to remove the length of the adjacent side to challenge your pupils.

      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

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      $$14^2=$$

      Correct Answer: 196, one hundred and ninety six

      Q2.
      Izzy has used her calculator to find the square root of 648. Which of these are correct for the given degree of accuracy?

      An image in a quiz
      Correct answer: 25.4 (truncated to 1 decimal place)
      30 (nearest whole number)
      Correct answer: 25.5 (3 significant figures)
      25.4 (1 decimal place)
      0.456 (3 decimal places)

      Q3.
      What type of triangle is this?

      An image in a quiz
      scalene triangle
      isosceles triangle
      equilateral triangle
      Correct answer: right-angled scalene triangle
      right-angled isosceles triangle

      Q4.
      If a square has an edge length of 19 cm, then its area is $$\text{ cm}^2$$.

      4.4
      38
      76
      Correct answer: 361

      Q5.
      A square has an area of 1024$$\text{ cm}^2$$. What is the edge length of the square?

      Correct Answer: 32 cm, 32

      Q6.
      A square has an area of 1369$$\text{ m}^2$$. What is the perimeter of this square?

      Correct Answer: 148 m, 148 metres

      6 Questions

      Q1.
      The hypotenuse is the __________ edge of a right-angled triangle and is always opposite the right angle.

      shortest
      Correct answer: longest

      Q2.
      Match the squares with the correct area.

      An image in a quiz
      Correct Answer:a,$$169\text{ cm}^2$$

      $$169\text{ cm}^2$$

      Correct Answer:b,$$25\text{ cm}^2$$

      $$25\text{ cm}^2$$

      Correct Answer:c,$$144\text{ cm}^2$$

      $$144\text{ cm}^2$$

      Q3.
      Given that 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 its longest side (the hypotenuse), a = ...

      An image in a quiz
      64
      161
      225
      Correct answer: 289

      Q4.
      Pythagoras' theorem as a formula is $$c^2=a^2+b^2$$, where $$c$$ is the hypotenuse. Which of the following are correct rearrangements of the formula?

      $$a^2=b^2+c^2$$
      $$b^2=a^2+c^2$$
      Correct answer: $$a^2=c^2-b^2$$
      Correct answer: $$c=\sqrt{a^2+b^2}$$
      $$c=a+b$$

      Q5.
      Work out the length of $$x$$.

      An image in a quiz
      Correct Answer: 37, thirty seven

      Q6.
      Work out the length of $$x$$.

      An image in a quiz
      Correct Answer: 20, twenty

      To help you plan your 10 maths lesson on: Checking and further securing understanding of Pythagoras' theorem, download all teaching resources for free and adapt to suit your pupils' needs...