Home › GCSE Maths › Geometry and Measures
Geometry and Measures
Geometry and Measures develops the language, constructions, transformations, mensuration, trigonometry and proof skills used across GCSE Mathematics.
The 20 lessons are arranged in five curriculum groups. Foundation and Higher routes are clearly signposted, while Higher-only lessons appear where the specification genuinely requires them.
For the Foundation route, follow shared lessons 1–12, 14–15 and 19. Higher learners also complete 13, 16–18 and 20, plus the Higher extensions within shared lessons.
Geometric Foundations and Construction
1. Geometric Language, Shapes and Symmetry Build the notation and shape properties used throughout GCSE geometry, including symmetry, coordinates and midpoint.
View Lesson →
2. Angles, Parallel Lines and Polygons Use angle facts, parallel-line relationships and polygon angle sums with clear reasons and short proofs.
View Lesson →
3. Constructions and Loci Construct bisectors and perpendiculars accurately, then interpret and combine loci to identify feasible regions.
View Lesson →
4. Bearings and Geometric Drawings Read, draw and calculate three-figure bearings and combine them with scale drawings and angle reasoning.
View Lesson →
Transformations, Congruence and Similarity
5. Reflections, Rotations and Translations Construct and describe isometries on coordinate grids, with a clearly marked Higher extension on combinations.
View Lesson →
6. Enlargements and Centres of Enlargement Construct and recover enlargements, including positive fractional factors, then extend to negative factors at Higher.
View Lesson →
7. Congruence, Similarity and Geometric Reasoning Use congruence criteria, similar-triangle ratios and clear geometric proofs, giving a reason for each step.
View Lesson →
Shape, Area and Volume
8. 3D Shapes, Nets, Plans and Elevations Interpret solids, nets, plans and elevations and reason about hidden dimensions and views.
View Lesson →
9. Perimeter and Area Develop perimeter and area methods for standard and composite shapes, including reverse and coordinate problems.
View Lesson →
10. Circles, Arcs and Sectors Use circle terminology, circumference, area, arc length, sector area and sector perimeter in forward and reverse problems.
View Lesson →
11. Surface Area and Volume of Prisms and Cylinders Use cross-sections, nets and formulae to calculate volume and exposed surface area of prisms and cylinders.
View Lesson →
12. Pyramids, Cones, Spheres and Composite Solids Work with curved and non-prismatic solids, including composite forms, reverse calculations and supplied-dimension frustums.
View Lesson →
13. Similar Shapes: Length, Area and Volume Connect linear scale factor to area and volume factors and solve reverse similarity problems.
View Lesson →
Pythagoras and Trigonometry
14. Pythagoras and Coordinate Distances Derive and apply Pythagoras in 2D, including coordinate distance and exact-root answers.
View Lesson →
15. Right-Angled Trigonometry and Exact Values Use SOHCAHTOA for sides and angles and learn the required exact trigonometric values.
View Lesson →
16. 3D Pythagoras and Trigonometry Extract right triangles from 3D solids to find lengths and line–plane angles.
View Lesson →
17. Sine Rule, Cosine Rule and Triangle Area Choose and apply non-right-triangle methods, including ½ab sin C and ambiguous-angle reasoning.
View Lesson →
Circle Theorems and Vectors
18. Circle Theorems and Circle Proofs Apply the full set of GCSE circle theorems and construct reasoned proofs from labelled diagrams.
View Lesson →
19. Vectors and Vector Arithmetic Represent displacement with vectors and use addition, subtraction and scalar multiplication in diagrams and coordinates.
View Lesson →
20. Vector Geometry and Proof Use vector routes, ratios and scalar multiples to prove parallelism, collinearity and geometric results.
View Lesson →
Related SumLogic lessons
Geometry builds on existing work in Units, Scale Drawings and Maps , Linear Graphs , Rearranging Formulae , Powers and Roots and Bounds and Error Intervals .
Graphs and coordinate mathematics in Algebra covers circle and tangent-line equations, function transformations and trigonometric graphs. Real-Life and Travel Graphs and the Higher lesson Areas Under Graphs and Accumulated Change are taught in Ratio, Proportion and Rates of Change.
