Geometry covers shape properties, angle relationships, circle theorems, transformations, and vectors. Circle theorems are a key Extended topic frequently tested in Papers 2 and 4.
Angles on a straight line = 180°. Angles at a point = 360°. Vertically opposite angles are equal. Parallel line angles: alternate (Z-shape), corresponding (F-shape), co-interior (C-shape, sum 180°). Interior angle sum of n-gon = (n−2) × 180°. Exterior angles sum to 360°.
Congruent: same shape and size (SSS, SAS, ASA, RHS). Similar: same shape, different size (AA, SAS ratio, SSS ratio). Scale factor k: lengths × k, areas × k², volumes × k³. Finding unknown sides and areas using similarity ratios.
Angle at centre = 2 × angle at circumference. Angle in semicircle = 90°. Angles in same segment are equal. Opposite angles of cyclic quadrilateral sum to 180°. Tangent perpendicular to radius at point of contact. Two tangents from external point are equal length. Alternate segment theorem (Extended).
Reflection: in a line (mirror line). Rotation: centre, angle, direction. Translation: by a vector. Enlargement: centre and scale factor. Vectors (Extended): position vectors, addition/subtraction, scalar multiplication, magnitude |v| = √(x² + y²), parallel vectors, midpoint and section formulas.
For Extended, you need all seven theorems listed above plus the alternate segment theorem. For Core, the main ones are: angle at centre = 2 × angle at circumference, angle in semicircle = 90°, and tangent ⊥ radius. In exams, always state which theorem you are using in your working — marks are awarded for correct identification.
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