📏 GCSE Geometry
Master shapes, angles, and measurements with free exam-style questions and step-by-step worked solutions. From basic angle rules to trigonometry and circle theorems.
What is GCSE Geometry?
Geometry is the study of shapes, sizes, and positions. It's a highly visual part of GCSE Maths that tests your understanding of angles, area, perimeter, volume, and spatial reasoning.
Key areas include:
- Angles – angle facts, parallel lines, polygons
- Pythagoras' Theorem – finding missing sides in right-angled triangles
- Trigonometry – SOH CAH TOA for sides and angles
- Area, perimeter & volume – 2D and 3D shapes
- Circle theorems – Higher tier circle angle rules
- Transformations – reflections, rotations, translations, enlargements
📚 Geometry Topics
📐 Angles
Angle facts, angles in parallel lines, interior and exterior angles of polygons.
📏 Pythagoras' Theorem
Find missing sides in right-angled triangles. Apply to real-world problems.
📐 Trigonometry (SOHCAHTOA)
Find missing sides and angles using sin, cos, and tan ratios.
📦 Area & Perimeter
Calculate area and perimeter of triangles, quadrilaterals, circles, and compound shapes.
📦 Volume & Surface Area
Calculate volume and surface area of prisms, cylinders, cones, spheres, and pyramids.
⭕ Circle Theorems
Master the circle theorems for Higher tier: angles in circles, tangents, and chords.
🔄 Transformations
Perform and describe reflections, rotations, translations, and enlargements.
🧭 Bearings
Measure and calculate bearings. Combine with trigonometry for navigation problems.
➡️ Vectors
Add, subtract, and multiply vectors. Prove geometrical relationships.
💡 Geometry Tips for GCSE Success
1. Draw diagrams: Even if one is provided, redrawing and labelling helps you understand the problem.
2. State your angle facts: Always write "angles on a straight line = 180°" etc. to earn method marks.
3. Memorise key formulas: Area of circle (πr²), volume of sphere (⁴⁄₃πr³), and others not on the formula sheet.
4. Check units: Make sure your final answer uses the correct units (cm, cm², cm³ etc.).