GCSE Mathematics · Edexcel 1MA1 · Topic G.1
Properties and constructions
Key points
- Angle facts: vertically opposite angles are equal; in parallel lines, alternate angles are equal, corresponding angles are equal and co-interior angles sum to 180°. Always give reasons.
- Polygons: exterior angles sum to 360°; each exterior angle of a regular -gon is .
- Congruent shapes are identical (tests SSS, SAS, ASA, RHS); similar shapes are enlargements of each other.
- Constructions with ruler and compasses: perpendicular bisector, angle bisector, perpendicular from a point; loci are sets of points obeying a rule.
- Transformations: describe a reflection by its mirror line, a rotation by its centre, angle and direction, a translation by a column vector, and an enlargement by its centre and scale factor.
- Circle theorems (higher): angle at the centre is twice the angle at the circumference; angle in a semicircle is 90°; opposite angles of a cyclic quadrilateral sum to 180°; tangent ⟂ radius; alternate segment theorem.
- Know properties of quadrilaterals and how to sketch plans and elevations of 3D shapes.
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This sub-topic is about the properties of shapes and the reasoning that uses them: angle facts, polygons, congruence and similarity, constructions, loci and transformations, with circle theorems at Higher tier. Many marks come from giving a…
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