GCSE Maths: Geometry and Measures Revision Guide

Angle facts

Angles on a straight line sum to 180°, angles around a point sum to 360°, and angles in a triangle sum to 180°. Alternate angles (Z-angles) and corresponding angles (F-angles) on parallel lines are equal.

Pythagoras' theorem

For a right-angled triangle, a² + b² = c², where c is the hypotenuse (the longest side, opposite the right angle). Use this to find a missing side when you know the other two.

Trigonometry

In a right-angled triangle, SOH CAH TOA gives the relationships: sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent. Use these to find missing sides or angles.

Area and volume

Know the area formulas for common shapes (rectangle, triangle, circle, parallelogram, trapezium) and volume formulas for common 3D solids (cuboid, prism, cylinder), including using πr² for the area of a circle.

Common mistakes

• Using Pythagoras on a triangle that isn't right-angled.
• Mixing up which sides are opposite, adjacent and hypotenuse in trigonometry.
• Forgetting units, or not converting between units (e.g. cm and m) before calculating.