Conventional geometric terms and notations
Geometry has its own dictionary. Getting the vocabulary right is essential for understanding questions and writing precise answers.
Points, lines, line segments and rays
- Point — a position with no size. Labelled with a capital letter (e.g. A).
- Line — extends infinitely in both directions. Labelled by two points or a lowercase letter (e.g. line AB or line l).
- Line segment — a portion of a line between two endpoints. Notation AB (no extension).
- Ray — starts at a point and extends infinitely in one direction.
Angles
- Vertex — the corner where two lines meet. Plural: vertices.
- Angle — the amount of turn between two rays meeting at a vertex.
- Notation — angle ABC (∠ABC) means the angle at vertex B, formed by rays BA and BC.
Types of angle
| Type | Range |
|---|---|
| Acute | 0° < θ < 90° |
| Right | θ = 90° |
| Obtuse | 90° < θ < 180° |
| Straight | θ = 180° |
| Reflex | 180° < θ < 360° |
Lines in pairs
- Parallel lines — same direction, never meet. Marked with arrows (>) on each line. Notation: AB ∥ CD.
- Perpendicular lines — meet at 90°. Marked with a small square at the right angle. Notation: AB ⊥ CD.
Polygons and 3D vocabulary
- Polygon — closed flat shape with straight sides.
- Vertex / Vertices — corners.
- Edge — a line segment forming the boundary.
- Face — a flat surface of a 3D solid.
- Plane — a flat infinite 2D surface in 3D space.
Naming polygons
| Sides | Name |
|---|---|
| 3 | Triangle |
| 4 | Quadrilateral |
| 5 | Pentagon |
| 6 | Hexagon |
| 7 | Heptagon |
| 8 | Octagon |
| 10 | Decagon |
Conventional markings
- Equal sides marked with single, double or triple tick marks.
- Equal angles marked with single, double or triple arc marks.
- Right angles marked with a small square.
- Parallel sides marked with matching arrows.
⚠Common mistakes
- Confusing line with line segment — in GCSE work, "AB" usually means the segment, not the infinite line.
- Reflex angle confusion — the reflex angle is the one greater than 180° at the same vertex.
- Naming angles incorrectly — ∠ABC is the angle at B, NOT at A.
- Forgetting to mark parallel/equal/right in your own diagrams.
- Mixing 2D and 3D vocabulary — faces and edges are 3D terms; sides and corners are 2D.
➜Try this— Quick check
A regular hexagon has how many vertices, edges, and what is the size of each interior angle?
- Hexagon: 6 vertices, 6 edges. Interior angle = (6−2) × 180 / 6 = 120°.
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