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Angles:
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Angles on a straight line, around a point, vertically opposite
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Angles in triangles and quadrilaterals
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Parallel line angle rules (alternate, corresponding, etc.)
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Triangles and Quadrilaterals:
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Types and properties
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Interior and exterior angle sums
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Polygons:
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Sum of interior and exterior angles
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Regular polygons
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Congruence and Similarity:
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Proving triangles congruent (SSS, SAS, ASA, RHS)
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Similar shapes and scale factors
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Constructions and Loci:
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Constructing triangles using a ruler and compasses
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Perpendicular bisectors, angle bisectors
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Locus of points
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Plans and Elevations
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Perimeter and Area:
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Rectangles, triangles, parallelograms, trapeziums
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Compound shapes
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Circles:
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Area and circumference
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Parts of circles: radius, diameter, arc, sector, segment
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Calculating arc length and area of a sector
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Surface Area and Volume:
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Cuboids, prisms, cylinders
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Cones, spheres, pyramids
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Compound 3D shapes
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Units and Conversions:
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Metric unit conversions (mm, cm, m, km)
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Area and volume conversions (cm² to m², cm³ to m³, etc.)
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Translations (moving a shape)
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Reflections (mirror line)
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Rotations (centre of rotation, direction, degrees)
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Enlargements (scale factor, centre of enlargement — positive/negative/fractional)
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Describing transformations
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Combinations of transformations
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Circle Theorems:
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Angle at the centre = 2 × angle at the circumference
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Angles in the same segment
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Angle in a semicircle = 90°
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Cyclic quadrilateral (opposite angles sum to 180°)
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Tangents from a point are equal
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Radius meets tangent at 90°
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Alternate segment theorem
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Proof using circle theorems
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Vector notation and operations
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Vector diagrams
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Geometric proofs using vectors
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