Pythagoras theorem

Pythagoras' Theorem is one of the most important results in geometry, stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: **a² + b² = c²** This theorem appears in virtually every GCSE Maths exam, typically worth 3-5 marks. It's used in both Foundation and Higher tier papers. **Key terminology:** - **Hypotenuse** - the longest side, opposite the right angle - **Right angle** - exactly 90° - **Pythagorean triple** - whole number solutions like 3, 4, 5 or 5, 12, 13 **Common question types:** 1. Finding the hypotenuse given two shorter sides 2. Finding a shorter side given the hypotenuse and one side 3. 3D problems (using Pythagoras twice) 4. Real-world contexts (ladders, distances, diagonals) 5. Proving whether a triangle is right-angled **Exam tips:** - Draw a diagram if one isn't provided - Label the hypotenuse clearly (always opposite the right angle) - When finding the hypotenuse: add the squares - When finding a shorter side: subtract the squares - Give your answer to an appropriate degree of accuracy (usually 1 or 3 significant figures)