Knowledge organisers

Geometry: Cambridge IGCSE Maths (0580) knowledge organiser

Everything to know about geometry on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Alternate angles: Equal angles on opposite sides of a line crossing two parallel lines (a Z shape).
Exterior angle: The angle between one side of a polygon and the next side extended; they add to 360°.
Similar shapes: Same shape, different size: all lengths are multiplied by the same scale factor.
Tangent to a circle: A line touching the circle at one point; it is perpendicular to the radius there.

Key formulas

Angles: on a straight line \(180^\circ\); around a point \(360^\circ\); in a triangle \(180^\circ\)
Polygons (\(n\) sides)	\(\text{interior sum}=(n-2)\times180^\circ,\) \(\text{exterior angle (regular)}=\tfrac{360^\circ}n\)
Circle theorems: angle in a semicircle = 90°; tangent ⟂ radius
More circle theorems: angle at centre = 2 × angle at circumference; angles in the same segment are equal; opposite angles of a cyclic quadrilateral sum to 180°; alternate segment theorem; tangents from a point are equal; the perpendicular bisector of a chord passes through the centre
Similar shapes, scale factor \(k\): lengths \(\times k\)
Similar shapes: areas \(\times k^2\), volumes \(\times k^3\)

Worked example

Find the size of each interior angle of a regular octagon.

Exterior angle = 360° ÷ 8 = 45°
Interior angle = 180° − 45°

Answer: 135°

Common mistakes

Map scales: not converting centimetres to kilometres
Bearings: the wrong angle, or measured from the wrong line

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Use geometrical terms for angles, lines, polygons, the parts of a circle and solids correctly when describing shapes and solving problems.
Use angle facts for lines, points, triangles and quadrilaterals to find missing angles, giving a geometric reason for each step.
Use the scale factor of similar shapes to calculate missing lengths, including triangles that share an angle or have parallel sides.
Use the circle properties of chords equidistant from the centre and of equal tangents from an external point, together with symmetry, to find lengths and angles.
Solve problems and give simple explanations involving similarity.
Identify planes of symmetry and axes of rotational symmetry of prisms, cylinders, pyramids and cones.

The printable sheet

Geometry knowledge organiser for Cambridge IGCSE Maths (0580): one A4 page of key definitions, formulas, a worked example and common mistakes — Geometry knowledge organiser (Cambridge IGCSE Maths (0580)), A4. Download the PDF.

Revise it next

Other Cambridge IGCSE Maths (0580) topics: Number · Algebra and graphs · Coordinate geometry · Mensuration · Trigonometry · Transformations and vectors · Probability · Statistics · All Cambridge IGCSE Maths (0580) organisers