Geometry ToolkitCambridge IGCSE Maths: Revision notes
Section 1
What basic geometrical terms must I know?
- Point: an exact location with no size
- Vertex: a corner where two or more lines/edges meet
- Line: a straight one-dimensional path between points
- Plane: a flat two-dimensional surface
- Parallel: lines that never meet and stay the same distance apart
- Perpendicular: lines that meet at exactly 90°
- Perpendicular bisector: a line that cuts another line exactly in half at a right angle
- Bearing: a direction measured clockwise from north as a three-figure angle
- Right angle: exactly 90°; acute: less than 90°; obtuse: between 90° and 180°; reflex: between 180° and 360°
- Interior angle: an angle inside a shape; exterior angle: the angle between a side and the extension of the next side
- Similar: same shape, proportional sides, equal angles; congruent: identical in shape and size
- Scale factor: the multiplier that relates corresponding lengths of similar shapes
Key termsperpendicular bisectorsimilarcongruentscale factor
Section 2
How do I classify triangles and quadrilaterals?
Triangles (by side/angle properties):
- Equilateral: all three sides and angles equal (60° each)
- Isosceles: two equal sides and two equal base angles
- Scalene: all sides and angles different
- Right-angled: contains one 90° angle
Special quadrilaterals:
| Shape | Key property |
|---|---|
| Square | 4 equal sides, 4 right angles |
| Rectangle | 2 pairs equal sides, 4 right angles |
| Rhombus | 4 equal sides, opposite angles equal |
| Parallelogram | 2 pairs of parallel, equal sides |
| Kite | 2 pairs of adjacent equal sides |
| Trapezium | exactly one pair of parallel sides |
Key termsisoscelesrhombustrapezium
Section 3
What polygon, net and solid vocabulary do I need?
Polygons: regular (all sides/angles equal) or irregular; named by number of sides — pentagon (5), hexagon (6), octagon (8), decagon (10).
Nets: 2D shapes that fold into 3D solids, used to calculate surface area.
Solids: cube, cuboid, prism, cylinder, pyramid, cone, sphere, hemisphere (not required at Core), and frustum (a solid formed by cutting the top off a cone or pyramid).
Key termsregular polygonfrustum
Section 4
What circle vocabulary do I need?
- Centre: the fixed middle point of a circle
- Radius: distance from centre to circumference
- Diameter: a chord through the centre, twice the radius
- Circumference: the perimeter (boundary) of a circle
- Semicircle: half a circle, cut by a diameter
- Chord: a line joining two points on the circumference
- Tangent: a line touching the circle at exactly one point
- Arc: part of the circumference (major/minor at Extended)
- Sector: a region bounded by two radii and an arc
- Segment: a region bounded by a chord and an arc
Key termscircumferencesectorarc
Section 5
How do I measure and draw accurately?
- Use a ruler for every straight edge — never draw freehand
- Use a protractor to measure and draw angles precisely
- Label all given lengths and angles clearly on your diagram
- Give lengths and angles to a sensible degree of accuracy (usually 1 decimal place for angles, whole mm for lengths)
Exam tip
Even when a question doesn't ask you to draw, sketching a labelled diagram from a worded description helps you see the geometry clearly.
Must Know
- Angle types: acute (<90°), right (90°), obtuse (90°–180°), reflex (180°–360°)
- Similar shapes have equal angles and proportional sides; congruent shapes are identical
- Know all special quadrilaterals: square, rectangle, rhombus, parallelogram, kite, trapezium
- Polygon names: pentagon (5), hexagon (6), octagon (8), decagon (10) sides
- Circle vocabulary: radius, diameter, chord, tangent, arc, sector, segment
- Always use a ruler and protractor for accurate drawing and measuring
That's the notes covered.
Carry on to the next subtopic.