This mini-lesson covers Geometry for Cambridge IGCSE Mathematics (0580): angle properties, polygons, circle theorems, congruence & similarity, symmetry and constructions (Extended content included).
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Key facts: angles on a straight line sum to 180°, angles at a point sum to 360°, and the angles in a triangle sum to 180°. With parallel lines, corresponding and alternate angles are equal.
Isosceles: two equal sides give two equal base angles.
The interior angles of a polygon with n sides sum to (n − 2) × 180°. The exterior angles always sum to 360°.
Pentagon: (5 − 2) × 180 = 540°. Regular pentagon exterior angle = 360 ÷ 5 = 72°.
Core theorems: the angle at the centre is twice the angle at the circumference on the same arc; the angle in a semicircle is 90°; angles in the same segment are equal; opposite angles of a cyclic quadrilateral sum to 180°.
Tangent facts: a tangent meets a radius at 90°, and two tangents from a point are equal in length.
Congruent shapes are identical (same size and shape). Similar shapes have the same shape but a scale factor difference — corresponding angles equal, sides in proportion.
Two similar triangles with scale factor 3: a 5 cm side maps to 15 cm. Areas scale by 3² = 9.
Tap a polygon, then its interior-angle sum.
A shape has line symmetry (mirror lines) and rotational symmetry (order = how many times it looks the same in a full turn). Constructions use compass and straight edge — e.g. a perpendicular bisector or an angle bisector.
A square has 4 lines of symmetry and rotational symmetry of order 4.
Regular n-gon: n lines of symmetry and rotational symmetry of order n.
Sort each angle: is it exactly 90° (a right angle) or not? Tap it, then its box.
Angles: line 180°, point 360°, triangle 180°; parallel-line rules.
Polygons: interior sum (n − 2)×180°; exterior sum 360°.
Circle theorems: centre = 2 × circumference; semicircle 90°; cyclic quad opposite angles 180°.
Similarity: lengths ×k, areas ×k², volumes ×k³.
Symmetry: lines & rotational order; regular n-gon → n of each.
You've covered the Geometry essentials for Cambridge IGCSE Maths (0580). Press Finish to see your score.
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