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SavannahYear 8
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MathsShape and space27 min★★★ difficulty

Pythagoras' theorem

Pythagoras' theorem lets you find a missing side of a right-angled triangle without ever picking up a ruler.

Part of your national curriculum
  • Geometry and measures: Use Pythagoras' theorem to solve problems involving right-angled triangles

Lesson overview

What you'll learn in this lesson

Use Pythagoras' theorem to solve problems involving right-angled triangles

Key learning points

  • • The theorem
  • • Worked example: finding the hypotenuse
  • • Worked example: finding a leg

This lesson at a glance

  • 27 minutes
  • 14 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

pythagorastheoremproblemsinvolvingright-angled

Scroll down — the lesson carries on below

Part 1 of 14 · Discover7%
1

Watch & discover

Part 1 of 14

Watch first

Pythagoras' theorem

An English teaching video on this topic from Homeschool Pop. Watch it, then scroll down for the lesson.

In a nutshell

Use Pythagoras' theorem to solve problems involving right-angled triangles

2

Learning cycle

Part 2 of 14

Learning cycle 1 of 2

Part 1 · The theorem

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 14

Learn

The theorem

In a right-angled triangle, a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle) and a, b are the other two sides.

4

Explore the idea

Part 4 of 14

Learn

Worked example: finding the hypotenuse

A triangle has legs 6 cm and 8 cm. c² = 6² + 8² = 36 + 64 = 100. So c = √100 = 10 cm.

5

Quick check

Part 5 of 14

Quick check

A right-angled triangle has legs 6 cm and 8 cm. What is the hypotenuse?

6

Reset break

Part 6 of 14

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 14

Quick check

A triangle has hypotenuse 13 cm and one leg 5 cm. What is the other leg?

8

Learning cycle

Part 8 of 14

Learning cycle 2 of 2

Part 2 · Worked example: finding a leg

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 14

Learn

Worked example: finding a leg

A right-angled triangle has hypotenuse 13 cm and one leg 5 cm. b² = 13² - 5² = 169 - 25 = 144, so b = √144 = 12 cm.

10

Quick check

Part 10 of 14

Quick check

In a²+b²=c², which side is c?

11

Challenge round

Part 11 of 14

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Challenge round

Part 12 of 14

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

In a ____ triangle, a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle) and a, b are the other two sides.

13

Mastery quiz

Part 13 of 14

Marked quiz

End of lesson quiz: Pythagoras' theorem

3 questions, marked with the reasoning shown. No timer.

  1. 1. A right-angled triangle has legs 6 cm and 8 cm. What is the hypotenuse?

  2. 2. A triangle has hypotenuse 13 cm and one leg 5 cm. What is the other leg?

  3. 3. In a²+b²=c², which side is c?

14

Lesson round-up

Part 14 of 14

Lesson round-up

Ready when you are

Quiz score

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Points this lesson

0

Best run

0 in a row

Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 14 · Watch & discover

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    Use Pythagoras' theorem to solve problems involving right-angled triangles

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