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Pythagoras' theorem - GCSE Maths Definition

Reviewed by: Dan Finlay

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Pythagoras' theorem is a formula that allows us to work out any length in a right-angled triangle if we know the other two.

The theorem is easiest to understand using its formula,

a squared space space plus b squared space space equals c squared

c is the hypotenuse (the longest side, which is always opposite the right angle); a and b are the other two sides (in no particular order).

Pythagoras' theorem can be applied by substituting in the values for the two known sides, then rearranging/solving as necessary to find the unknown side.

Pythagoras' theorem is very well known, and as such, you may see variations of the formula; for example, a2 = b2 + c2 (in which case a is the hypotenuse) and the use of different letters, especially h for the hypotenuse. All such formulae are equivalent. Once you are able to apply Pythagoras' theorem to right-angled triangles, further uses can be explored, such as finding the distance between two points.

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Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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