Chapter 9: Pythagoras and geometric proof
Pythagoras links the three sides of every right-angled triangle and can be justified using areas of squares.
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 relationship
- • Find a side
- • Problem solving
This lesson at a glance
- 32 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
Chapter 9: Pythagoras and geometric proof
Pythagoras links the three sides of every right-angled triangle and can be justified using areas of squares.
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 relationship
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 17
Learn
The relationship
For a right-angled triangle, a²+b²=c², where c is the hypotenuse opposite the right angle. The theorem does not apply directly to non-right-angled triangles.
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
Find a side
With shorter sides 6 cm and 8 cm, c=√(36+64)=10 cm. If c=13 cm and one shorter side is 5 cm, the other is √(169−25)=12 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 · Problem solving
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 17
Learn
Problem solving
Sketch and label the right triangle, identify the hypotenuse, substitute with units, calculate, then round only at the end. Compare the answer with the longest-side condition.
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.
For a ____ triangle, a²+b²=c², where c is the hypotenuse opposite the right angle.
The ____ does not apply directly to non-right-angled triangles.
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: Chapter 9: Pythagoras and geometric proof
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
Quiz score
Not sat
Games
Not played
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 LunaPart 1 of 17 · Watch & discover
How this is going
- Not looked at yet
Use Pythagoras' theorem to solve problems involving right-angled triangles