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Pythagoras' Theorem is one of the most important results in geometry. It links the three sides of a right-angled triangle and appears throughout Edexcel GCSE Mathematics — from straightforward calculations to multi-step problem solving. Higher tier extends to 3D applications.
| Term | Meaning |
|---|---|
| Right-angled triangle | A triangle containing one 90° angle |
| Hypotenuse | The longest side, opposite the right angle |
| Pythagorean triple | A set of three positive integers that satisfy a² + b² = c² (e.g. 3, 4, 5) |
In any right-angled triangle with hypotenuse c and shorter sides a and b:
a² + b² = c²
This means: the square of the hypotenuse equals the sum of the squares of the other two sides.
Edexcel Formula Sheet: Pythagoras' Theorem is NOT on the Edexcel formula sheet — you must memorise it.
Consider a right-angled triangle with sides a, b and hypotenuse c. If you draw a square on each side:
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