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Geometry & MeasuresIntroduction

The Ancient Discovery

Part of Pythagoras' Theorem · GCSE GCSE Mathematics revision

This introduction covers The Ancient Discovery within Pythagoras' Theorem for GCSE Mathematics. Revise Pythagoras' Theorem in Geometry & Measures for GCSE Mathematics with 17 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 4 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 4

Practice

17 questions

Recall

3 flashcards

The Ancient Discovery

Over 2,500 years ago, Pythagoras discovered a beautiful relationship in right-angled triangles: if you square the two shorter sides and add them together, you get the square of the longest side (the hypotenuse). This works for EVERY right-angled triangle in the universe!

Visual: Pythagoras' Theorem

Diagram showing Pythagoras theorem with squares on each side of a right triangle. a² + b² = c² where c is the hypotenuse. Includes formulas for finding hypotenuse and shorter sides.

Keep building this topic

Read this section alongside the surrounding pages in Pythagoras' Theorem. That gives you the full topic sequence instead of a single isolated revision point.

The FormulaWorked Example: Finding the HypotenuseKnowledge Organiser: Pythagoras' Theorem

Practice Questions for Pythagoras' Theorem

In a right-angled triangle with legs a and b and hypotenuse c, which formula is Pythagoras' theorem?

  • A. a + b = c
  • B. a² + b² = c²
  • C. a² − b² = c²
  • D. a × b = c²
1 markfoundation

A triangle has sides of length 5 cm, 12 cm, and 13 cm. Explain how you can tell, without measuring any angles, whether this triangle contains a right angle.

2 marksstandard

Quick Recall Flashcards

Pythagoras Theorem
a² + b² = c² where c is hypotenuse
Pythagoras' Theorem
a² + b² = c² (where c is the hypotenuse)

17 questions on Pythagoras' Theorem — practise free

Instant marking, adaptive difficulty, and 3 spaced repetition flashcards. Free until your GCSEs.

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The Formula