Knowledge Organiser: Pythagoras' Theorem
Part of Pythagoras' Theorem · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Pythagoras' Theorem 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 4 of 4 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 4 of 4
Practice
17 questions
Recall
3 flashcards
Knowledge Organiser: Pythagoras' Theorem
Key Terms
- Hypotenuse (c): The LONGEST side, opposite the right angle
- Right-angled triangle: A triangle with one 90° angle
- Pythagorean triple: A set of whole numbers satisfying a² + b² = c² (e.g. 3, 4, 5)
- Square root: The inverse of squaring; √25 = 5
Must-Know Facts
- Only works for RIGHT-ANGLED triangles
- c is ALWAYS the hypotenuse (longest side, opposite the right angle)
- Common triples: 3-4-5, 5-12-13, 8-15-17
- To find a shorter side: a = √(c² − b²)
- Check: the square of the two shorter sides must sum to the square of the longest
Key Formulas
- a² + b² = c²
- Hypotenuse: c = √(a² + b²)
- Shorter side: a = √(c² − b²)
Common Mistakes
- Adding instead of subtracting for shorter side: To find a shorter side, use a² = c² − b² (subtract), not c² + b²
- Identifying the hypotenuse: The hypotenuse is always opposite the right angle and always the longest side
- Not square rooting at the end: a² + b² = c² gives c², so take √ to find c itself
- Using Pythagoras on non-right-angled triangles: Only valid for right-angled triangles — use sine/cosine rule otherwise
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Practice Questions for Pythagoras' Theorem
In a right-angled triangle with legs a and b and hypotenuse c, which formula is Pythagoras' theorem?
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.
Quick Recall Flashcards
17 questions on Pythagoras' Theorem — practise free
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