Pythagoras' Theorem
Use Pythagoras' theorem to find a missing side in a right-angled triangle and solve problems.
Overview
Pythagoras' theorem links the three sides of a right-angled triangle: the square of the longest side (the hypotenuse) equals the sum of the squares of the other two. In Year 9 students use it to find a missing side and to solve real problems involving distance. It is a cornerstone of IGCSE geometry and trigonometry.
What You Will Learn
- State and understand Pythagoras’ theorem, a² + b² = c²
- Identify the hypotenuse as the side opposite the right angle
- Find the hypotenuse given the two shorter sides
- Find a shorter side given the hypotenuse and one other side
- Use Pythagoras’ theorem to solve problems involving distance
Key Vocabulary
Common Mistakes to Avoid
- Using the wrong side as the hypotenuse
- Adding the squares when you should subtract to find a shorter side
- Forgetting to square root at the end
- Mixing up which sides are a, b and c
What Comes Next
At IGCSE this is used throughout the Trigonometry topic, including in three dimensions and alongside the sine and cosine rules.
Frequently Asked Questions
Which side is the hypotenuse?
The hypotenuse is the longest side of a right-angled triangle, and it is always the side opposite the right angle. In a² + b² = c², the hypotenuse is c.
How do I find a shorter side, not the hypotenuse?
Rearrange the formula to subtract. If c is the hypotenuse, then a² = c² − b². Work out the subtraction first, then take the square root.
Study This Topic
Topic Details
- Stage
- Year 9
- Strand
- Geometry and Measure
- Framework ref
- 9Gg
- Difficulty
- Medium
Build strong foundations in Pythagoras' Theorem
A free trial class with Teacher Rig helps your Year 9 child master Pythagoras' Theorem now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Pythagoras' Theorem develops in IGCSE Trigonometry (Cambridge 0580) →