Pythagoras' Theorem

This lesson covers Pythagoras' Theorem for AQA GCSE Mathematics. You will learn how to find the hypotenuse, find a shorter side, and apply the theorem in real-world contexts. Higher-tier students will also study 3D Pythagoras. This is one of the most important topics in GCSE Mathematics and appears on almost every exam paper.

---

What Is Pythagoras' Theorem?

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

a squared + b squared = c squared

where c is the hypotenuse (the longest side, opposite the right angle) and a and b are the other two sides.

graph LR
    A[Right-angled triangle] --> B[Identify the hypotenuse longest side]
    B --> C{What are you finding?}
    C -->|Hypotenuse| D[c = square root of a squared + b squared]
    C -->|Shorter side| E[a = square root of c squared - b squared]

Exam Tip: The hypotenuse is ALWAYS the side opposite the right angle. It is always the longest side. If the question does not explicitly label the right angle, look for the small square symbol.

---

Finding the Hypotenuse