E4.1 Geometrical terms
- Syllabus
- 0580–2028–2029
- Topic
- E4.1
- Level
- Extended
Learning objectives
E4.1.1Geometrical terms• Use and interpret geometrical terms including point, vertex, line, plane, parallel, perpendicular, perpendicular bisector, bearing, angle types, similarity, congruence and scale factor.E4.1.2Shapes, polygons, nets and solids• Use and interpret the vocabulary of triangles, special quadrilaterals, regular and irregular polygons, nets and common solids including prisms, pyramids, cones, spheres, hemispheres and frustums.E4.1.3Circle vocabulary• Use and interpret circle vocabulary including centre, radius, diameter, circumference, semicircle, chord, tangent, major and minor arcs, sector and segment.
Read geometrical language precisely
Geometrical terms describe an object, a relationship or a transformation exactly. Reading the term first tells you which features in a diagram matter.
| Term | Precise meaning |
|---|---|
| point / vertex | an exact position / a corner where sides or edges meet |
| line / plane | a straight one-dimensional path / a flat two-dimensional surface extending without end |
| parallel / perpendicular | lines that never meet / lines meeting at 90∘ |
| perpendicular bisector | a line crossing a segment at its midpoint and at 90∘ |
| bearing | a clockwise angle from north, written with three figures |
Angle types are set by size: acute is less than 90∘; right is 90∘; obtuse is between 90∘ and 180∘; reflex is between 180∘ and 360∘. Interior angles lie inside a shape; exterior angles are formed outside when a side is extended.
Congruent shapes have the same shape and size. Similar shapes have the same shape but may differ in size; every corresponding length changes by one scale factor while corresponding angles stay equal.
A perpendicular bisector does both jobs—bisects and meets at a right angle. Parallel-looking lines are not guaranteed parallel unless the diagram or markings say so, and candidates are not required here to prove that two shapes are congruent.
Classify shapes and solids by their properties
Classify a shape from stated properties, not from how its sketch happens to look. More than one name can be true, so use the most specific name supported by the information.
| Family | Examples and distinguishing features |
|---|---|
| triangles | equilateral: 3 equal sides; isosceles: at least 2 equal sides; scalene: no equal sides; right-angled: one 90∘ angle |
| quadrilaterals | square, rectangle, kite, rhombus, parallelogram and trapezium are distinguished by equal sides, parallel sides and right angles |
| polygons | closed straight-sided shapes; regular means every side and angle is equal, while irregular means they are not all equal |
Name common polygons by side count: pentagon 5, hexagon 6, octagon 8 and decagon 10. A diagonal joins two non-adjacent vertices.
For solids, distinguish faces or curved surfaces, edges and vertices. A prism has the same cross-section all along its length; a pyramid narrows from a polygonal base to one vertex. Other required names include cube, cuboid, cylinder, cone, sphere, hemisphere and frustum. A net is a flat arrangement that folds to make a solid.
A quadrilateral with two pairs of parallel sides and all four sides equal is a rhombus. If it also has four right angles, the more specific name is square. A solid with a trapezium cross-section unchanged through its length is a trapezoidal prism.
A cylinder is not a prism under this syllabus vocabulary, because its cross-section boundary includes a curve. A frustum is the part left after the top of a cone or pyramid is cut off by a plane parallel to its base.
Name the parts of a circle
Circle vocabulary identifies whether a line, curve or region is measured from the centre, lies on the circumference or cuts off part of the circle.
| Term | Meaning |
|---|---|
| radius | segment from the centre to the circumference |
| diameter | chord through the centre; its length is twice the radius |
| chord | segment joining two points on the circumference |
| tangent | line touching the circle at exactly one point |
| circumference | the circle's boundary |
| semicircle | half a circle, bounded by a diameter and half the circumference |
An arc is part of the circumference: the minor arc is the shorter route between two points and the major arc is the longer route. A sector is the region between two radii and an arc. A segment is the region between a chord and an arc.
If AB joins two points on the circumference, it is a chord. If it passes through the centre, it is also a diameter. The region swept out between radii OA and OB is a sector, while the region cut off by chord AB is a segment.
A secant-like line crossing the circle at two points is not a tangent. Do not swap sector and segment: a sector has two straight radius boundaries; a segment has one straight chord boundary.