Pythagoras' Theorem — Year 9 Revision Notes
These notes cover Pythagoras' theorem and how to find the hypotenuse or a shorter side of a right-angled triangle — all at Year 9 (Stage 9) level.
The theorem
In a right-angled triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle) and a and b are the two shorter sides. The theorem only works for right-angled triangles.
Key Facts & Formulas
- a² + b² = c²
- c is the hypotenuse
Tips
- Label the hypotenuse first — it is opposite the right angle.
- The theorem only applies to right-angled triangles.
Finding the hypotenuse
To find the hypotenuse, square the two shorter sides, add them, then take the square root. For sides 3 and 4: 3² + 4² = 9 + 16 = 25, so the hypotenuse is √25 = 5.
Key Facts & Formulas
- c = √(a² + b²)
- √(3² + 4²) = 5
Tips
- Add the squares when finding the hypotenuse.
- Do not forget the final square root.
Finding a shorter side
To find a shorter side, subtract the square of the known shorter side from the square of the hypotenuse, then square root. If the hypotenuse is 13 and one side is 5: 13² − 5² = 169 − 25 = 144, so the other side is √144 = 12.
Key Facts & Formulas
- a = √(c² − b²)
- √(13² − 5²) = 12
Tips
- Subtract the squares when finding a shorter side.
- Check the hypotenuse is the largest value.
Revision Checklist
- I can state Pythagoras’ theorem and identify the hypotenuse
- I can find the hypotenuse of a right-angled triangle
- I can find a shorter side using the theorem
- I can use Pythagoras’ theorem to solve distance problems
Frequently Asked Questions
Does Pythagoras' theorem work for all triangles?
No. It only works for right-angled triangles, because it relies on there being a right angle opposite the hypotenuse. For other triangles you need the sine or cosine rule, which come later at IGCSE.
Build strong foundations in Pythagoras' Theorem
A free trial class with Teacher Rig helps your Year 9 child master Pythagoras' Theorem now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Pythagoras' Theorem develops in IGCSE Trigonometry (Cambridge 0580) →