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
- 17 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 17
Visual introductionPicture this
Pythagoras' theorem
Pythagoras' theorem lets you find a missing side of a right-angled triangle without ever picking up a ruler.
In a nutshell
Use Pythagoras' theorem to solve problems involving right-angled triangles
Learning cycle
Part 2 of 17
Learning cycle 1 of 2
Part 1 · The theorem
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
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.
Reset break
Part 4 of 17
Pause
That's sitting 1 of 4 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.
Explore the idea
Part 5 of 17
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.
Quick check
Part 6 of 17
Quick check
Part 7 of 17
Reset break
Part 8 of 17
Pause
That's sitting 2 of 4 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.
Learning cycle
Part 9 of 17
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.
Explore the idea
Part 10 of 17
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.
Quick check
Part 11 of 17
Reset break
Part 12 of 17
Pause
That's sitting 3 of 4 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.
Challenge round
Part 13 of 17
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
Challenge round
Part 14 of 17
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.
Challenge round
Part 15 of 17
Game · Recall cards
A right triangle has shorter sides 6 and 8. Find c.
Card 1 of 4
Mastery quiz
Part 16 of 17
Marked quiz
End of lesson quiz: Pythagoras' theorem
4 questions, marked with the reasoning shown. No timer.
1. A right triangle has shorter sides 6 and 8. Find c.
2. The hypotenuse is 13 and one side is 5. Find the other.
3. Which side is c?
4. A right-angled triangle has legs 6 cm and 8 cm. What is the hypotenuse?
Lesson round-up
Part 17 of 17
Lesson round-up
Ready when you are
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Use Pythagoras' theorem to solve problems involving right-angled triangles