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C4.1 Geometrical Terms

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Geometry questions are marked on precise vocabulary as much as on correct reasoning. Losing a mark for writing "diamond" instead of "rhombus," or "corner" instead of "vertex," is one of the most avoidable ways to drop marks in this syllabus.

01 — Explanation

What do point, line and angle terms mean?

A point is an exact position, usually marked with a dot and a capital letter. A vertex (plural vertices) is where two lines or edges meet — the corner of a shape. A line segment has two fixed endpoints, while a full line extends forever.

Two lines are parallel ( $\parallel$ ) if they stay the same distance apart forever without meeting, and perpendicular ( $\perp$ ) if they cross at exactly $90^\circ$ .

Angles are classified by size:

\text{acute: } 0^\circ < \theta < 90^\circ \qquad \text{obtuse: } 90^\circ < \theta < 180^\circ \qquad \text{reflex: } 180^\circ < \theta < 360^\circ

An interior angle sits inside a shape between two adjacent sides; an exterior angle sits between one side and the extension of the next.

Exam tip

a bearing is a direction measured clockwise from north, always written with three digits — $072^\circ$ , not $72^\circ$ .

02 — Explanation

How are triangles and quadrilaterals named?

Triangles are named by sides and angles:

Equilateral — all 3 sides equal, all angles $60^\circ$ .
Isosceles — exactly 2 sides equal, base angles equal.
Scalene — no sides or angles equal.
Right-angled — contains a $90^\circ$ angle.

Quadrilaterals are distinguished by which sides are equal or parallel:

Square — 4 equal sides, 4 right angles.
Rectangle — opposite sides equal, 4 right angles.
Parallelogram — opposite sides equal and parallel.
Rhombus — 4 equal sides, opposite sides parallel, angles not necessarily $90^\circ$ .
Kite — two pairs of adjacent equal sides.
Trapezium — exactly one pair of parallel sides.

03 — Explanation

What are polygons, nets and solids called?

A polygon is named by its number of sides, and is regular if all its sides and angles are equal, or irregular otherwise:

Sides	5	6	8	10
Name	Pentagon	Hexagon	Octagon	Decagon

A net is a flat 2D shape that folds up into a 3D solid. Every solid is built from faces (its flat or curved outer surfaces), edges (where two faces meet), and vertices (corner points). The Core tier solids are the cube, cuboid, prism, cylinder, pyramid, cone and sphere.

Net of a cube:              Net of a square-based pyramid:
   ┌───┐                            ▲
   │   │                          ╱ │ ╲
┌──┼───┼──┬───┐                 ╱  │  ╲
│  │   │  │   │                ┌───┴───┐
└──┴───┴──┴───┘                │ square│
   │   │                       │  base │
   └───┘                       └───────┘

04 — Explanation

What vocabulary describes the parts of a circle?

Centre — the fixed point every point on the circle is equidistant from.
Radius (plural radii) — a line from the centre to the circumference.
Diameter — a line through the centre joining two points on the circumference, $d = 2r$ .
Circumference — the boundary length of the circle.
Chord — a line joining two points on the circumference that does not pass through the centre.
Tangent — a straight line touching the circle at exactly one point.
Arc — part of the circumference.
Sector — a "pizza-slice" region enclosed by two radii and an arc.
Segment — a region enclosed by a chord and an arc.

Common mix-up: a sector is bounded by two radii (like a pizza slice through the centre); a segment is bounded by a chord (a straight cut that never touches the centre). A diameter is just a special chord — the only one that passes through the centre.

05 — Explanation

Exam-style practice

(a) A quadrilateral has exactly one pair of parallel sides. State its name.

(b) A straight line touches a circle at one point without crossing into its interior. State its name.

Solution

(a) Exactly one pair of parallel sides defines a trapezium.

(b) A line touching a circle at a single point is a tangent.