Maths
Pythagoras' theorem — quick study summary
GCSE MathsIGCSE Maths
In any right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². It works in reverse too — if a² + b² = c², the triangle is right-angled.
Key points
- Only applies to right-angled triangles
- Hypotenuse (c) is always opposite the right angle and is the longest side
- Pythagorean triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25)…
- Used for distance between two points in coordinate geometry
Practice quiz
Click each question to reveal the answer.
1. A right triangle has legs of length 6 and 8. What is the hypotenuse?
- 7
- 10
- 14
- 100
Answer: 10
√(36+64) = √100 = 10.
2. If c = 13 and one leg is 5, what is the other leg?
Answer: 12
√(169−25) = √144 = 12.
3. Does (3, 4, 5) form a right triangle?
Answer: Yes
9 + 16 = 25, so a² + b² = c².
Last reviewed: May 2026