Pythagoras

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Pythagoras' Theorem

Pythagoras' theorem lets us find a missing side of a right-angled triangle when we know the other two sides. It ONLY works for right-angled triangles!

Key Points:

The theorem is: a² + b² = c² (where c is the hypotenuse)
The hypotenuse is the longest side - it's opposite the right angle
To find the hypotenuse: ADD the squares, then square root
To find a shorter side: SUBTRACT the squares, then square root

Top Tips

  • Always draw and label the triangle if one isn't given
  • Remember to give your answer to the correct number of decimal places or significant figures
  • Include UNITS in your answer (cm, m, km, etc.)

Worked Examples

1Step 1: Identify what we know: a = 3 cm, b = 4 cm, c = ? (hypotenuse)
2Step 2: Write Pythagoras' theorem: a² + b² = c²
3Step 3: Substitute the values: 3² + 4² = c²
4Step 4: Calculate the squares: 9 + 16 = c²
5Step 5: Add: 25 = c²
6Step 6: Square root both sides: c = √25 = 5 cm
Answer: 5 cm

🎬 Video Tutorials

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Pythagoras Theorem Explained

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GCSE Maths Tutor - Techniques and strategies for using Pythagoras theorem.

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Pythagoras - Full Introduction

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Complete introduction to the formula and how to use it (for 2026/27 exams).

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Pythagoras Exam Questions

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Key skills and challenge-style exam questions with worked solutions.

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Rules to Follow

💡 Click on any rule to see more details!

The Formula

a² + b² = c² where c is the HYPOTENUSE (the longes...

Finding Hypotenuse

c = √(a² + b²). Square both short sides, ADD them,...

Finding Short Side

a = √(c² - b²). Square the two known sides, SUBTRA...

Identify Hypotenuse

The hypotenuse is ALWAYS: 1) The longest side, 2) ...

Common Trap

Don't forget to SQUARE ROOT at the end! Many stude...