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Pythagoras' theorem, a² + b² = c², relates the sides of a right-angled triangle. This topic finds a missing side and applies it to lengths, coordinates and 2D and 3D problems. It's examined right across GCSE and iGCSE Maths. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
For the hypotenuse, square the two shorter sides and add. For a shorter side, square the hypotenuse and subtract. Take the square root at the end. Adding when you should subtract is the usual error, so check which side is longest first.
Before you start
This builds directly on squares, roots and right-angled triangles. It underpins trigonometry and 3D problems. It appears at Foundation and Higher tier.
What you learn
In any right-angled triangle, the three side lengths are linked by a² + b² = c². It lets you find a missing side whenever you know the other two. In a right-angled triangle, the longest side — the hypotenuse — is opposite the right angle. To find a shorter side, rearrange the rule to a² = c² − b² — you subtract instead of add. Many problems hide a right-angled triangle — straight-line distances, ladders, and diagonals. The course works through pythagoras’ theorem, finding a shorter side and using Pythagoras in problems. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Pythagoras' Theorem is part of the Geometry strand of our free GCSE maths courses, studied in Foundation tier. The course is built from 3 concept sections, 2 worked examples and 3 check points before the exam-style set. Related topics students usually take next include Sine & Cosine Rule, Transformations and Trigonometry. You can drill this strand further on the Geometry revision engine, with your accuracy saved to your skill tree.
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