New
New
Year 10
Foundation

Checking and further securing understanding of Pythagoras' theorem

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

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New
New
Year 10
Foundation

Checking and further securing understanding of Pythagoras' theorem

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

Link copied to clipboard

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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. 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.


To help you plan your year 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...

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

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

6 Questions

Q1.
142=
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  cm2.
4.4
38
76
Correct answer: 361
Q5.
A square has an area of 1024 cm2. What is the edge length of the square?
Correct Answer: 32 cm, 32
Q6.
A square has an area of 1369 m2. 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 cm2

169 cm2

Correct Answer:b,25 cm2

25 cm2

Correct Answer:c,144 cm2

144 cm2

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 c2=a2+b2, where c is the hypotenuse. Which of the following are correct rearrangements of the formula?
a2=b2+c2
b2=a2+c2
Correct answer: a2=c2b2
Correct answer: c=a2+b2
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
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