G1: Geometric Notation
Use conventional terms and notation: points, lines, vertices, edges, planes, parallel, perpendicular, right angles, polygons, regular polygons
📋 Key Concepts
Definition: Geometric notation is a standard way of describing and labelling geometric figures using accepted mathematical symbols and terms.
Basic Terms
| Term | Notation | Description |
|---|---|---|
| Point | Capital letter (A, B, C) | A specific location, has no size |
| Line | AB or AB with arrow | Extends infinitely in both directions |
| Line segment | AB | Part of a line with two endpoints |
| Ray | AB with one arrow | Starts at A, extends through B |
| Angle | ∠ABC or θ | Formed by two rays meeting at a point |
Types of Lines
Parallel lines: AB ∥ CD (never meet)
Perpendicular lines: AB ⊥ CD (meet at 90°)
Perpendicular lines: AB ⊥ CD (meet at 90°)
📝 Points, Lines and Planes
Key Facts: A point has no dimensions (location only). A line has one dimension (length). A plane has two dimensions (length and width).
Example 1
Name the line segment from point A to point B.
Solution: The line segment is written as AB or BA. Both notations are correct since a line segment can be read in either direction.
Example 2
Write the notation for "line AB is parallel to line CD".
Solution: AB ∥ CD
The symbol ∥ means "is parallel to".
📝 Vertices and Edges
Definitions: A vertex (plural: vertices) is a corner point where edges meet. An edge is a line segment joining two vertices.
Example 3
A triangle has 3 vertices and 3 edges. A square has 4 vertices and 4 edges. A cube has 8 vertices and 12 edges.
📝 Polygons
Polygon: A closed 2D shape with straight sides. A regular polygon has all sides equal and all angles equal.
| Polygon | Sides | Regular Name |
|---|---|---|
| Triangle | 3 | Equilateral triangle |
| Quadrilateral | 4 | Square |
| Pentagon | 5 | Regular pentagon |
| Hexagon | 6 | Regular hexagon |
| Octagon | 8 | Regular octagon |
| Decagon | 10 | Regular decagon |
📝 Angles
Angle Notation: Angles are measured in degrees (°). The symbol ∠ is used to denote an angle, e.g., ∠ABC means the angle at B between BA and BC.
| Type | Size |
|---|---|
| Acute | 0° < angle < 90° |
| Right angle | 90° |
| Obtuse | 90° < angle < 180° |
| Reflex | 180° < angle < 360° |
| Straight line | 180° |
| Full turn | 360° |
Example 4
State the type of angle shown: 135°
Solution: 135° is between 90° and 180°, so it is an obtuse angle.
🧮 Worked Examples — Exam Style
Geometric notation questions are pure recall marks. Learn the symbols as a matching set — and always name lines/angles in the right letter order.
Line PQ is parallel to line RS. Write this in notation, and state the angle relationship.
Notation: PQ ∥ RS
Parallel lines never meet — marked with arrows on diagrams. Angles in a matching "Z" (alternate) or "F" (corresponding) position are equal.
B1 for the ∥ symbol used correctly. Angle facts linked to parallel lines are the usual follow-up question.
Write the angle ABC, and explain what the middle letter means.
Notation: ∠ABC (or just ABC in exam text).
The middle letter (B) is the VERTEX — the corner where the angle sits. ∠ABC means the angle between ray BA and ray BC.
B1 for ∠ABC with B identified as the vertex. Angle names in proofs must match this letter order.
Exam wording to expect: "Write down the notation for …", or reading a diagram that uses the symbols.
❓ Practice Questions
Q1: Write the notation for "line AB is perpendicular to line CD".
Q2: How many vertices does a pentagon have?
Q3: What type of angle is 45°?
Q4: Name a regular polygon with 6 sides.
Q5: How many edges does a cube have?
Q6: Write the notation for: triangle ABC is similar to triangle DEF
Q7: How many faces does a cube have?
Q6: Write the notation for: triangle ABC is similar to triangle DEF
Q7: How many faces does a cube have?
Q6: Write the notation for: triangle ABC is similar to triangle DEF
Q7: How many faces does a cube have?
✅ Answers
- AB ⊥ CD
- 5 vertices
- Acute angle
- Regular hexagon
- 12 edges
🧮 Worked Examples — Harder Exam Style
A prism has an L-shaped cross-section. State the meaning of the word cross-section, and name the prism type.
Cross-section: the face revealed by slicing the prism parallel to its ends — the same shape all the way through.
A prism is named by its cross-section, so this is an L-shaped prism (a non-convex hexagonal prism).
B1 for the meaning, B1 for the name. Volume-of-prism questions open with exactly this vocabulary, so the definition is load-bearing.
📋 Model Answers — Full Working
Every mark in GCSE maths comes from the working, not just the answer. These model answers show the lines a mark scheme expects to see.
Q1. AB ⊥ CD — the ⊥ symbol means perpendicular (meets at 90°)
Q2. A pentagon has 5 vertices (one per corner)
Q3. 45° is between 0° and 90° → acute
Q4. A regular polygon has all sides and angles equal; 6 sides → regular hexagon
Q5. A cube has 12 edges (4 on top, 4 on bottom, 4 vertical)
Q6. △ABC ∼ △DEF — the ∼ symbol means similar (same shape, different size); ≅ means congruent (identical)
Q7. 6 faces
📌 Key Facts to Memorise
- ⊥ perpendicular (meets at 90°) · ∥ parallel (never meets, marked with arrows)
- △ triangle · ∠ angle · ≅ congruent (identical) · ∼ similar (same shape)
- Angle ∠ABC: the MIDDLE letter is the vertex where the angle sits
- Polygon names by sides: 5 pentagon, 6 hexagon, 7 heptagon, 8 octagon, 10 decagon
- Regular = all sides AND all angles equal
- Cube: 6 faces, 12 edges, 8 vertices
🗺️ In the Exam
Notation itself is 1–2 marks a year, but the vocabulary gates the geometry marks: "using congruent triangles", "the vertex B", "regular hexagon" all assume it. Properties-of-shapes recall (faces/edges/vertices) is a reliable 1-mark line.
Links to: angle rules (G4), transformations (G), 3D shapes and nets (G).
🧭 Board Focus — AQA
Spec 8300. Three papers, each 80 marks and 1h30: Paper 1 non-calculator, Papers 2 and 3 calculator. Foundation/Higher tiers. Roughly a third of the marks sit under AO2 (reasoning) and AO3 (problem-solving), so show every line of working — method marks survive arithmetic slips.
Always check: specification details change — confirm paper structure and set texts against the current specification for your exam year.
🎯 Exam Tips
- Use capital letters for points (A, B, C)
- Remember: ∥ means parallel, ⊥ means perpendicular
- A regular polygon must have BOTH equal sides AND equal angles
- Right angles are marked with a small square in diagrams
- Learn the Greek letter names for angles (α, β, θ, etc.)
🧠 Problem-Solving Strategies
Problem-Solving
Read geometric notation carefully: AB means the line segment from A to B, AB̄ means the length of AB, and the arrow symbol means the ray or directed line. Equal tick marks on a diagram show equal lengths. Angle notation ∠ABC means the angle at vertex B between BA and BC. Always label diagrams systematically.
Multi-Step Problem
In triangle ABC, side AB = 2 × side BC. Side AC = AB + 1 cm. If BC = 4 cm, find the perimeter and state which type of triangle this could be if all angles are different.
Solution: BC = 4 cm, AB = 2 × 4 = 8 cm, AC = 8 + 1 = 9 cm. Perimeter = 4 + 8 + 9 = 21 cm. Since all three sides are different, it is a scalene triangle (confirmed by all angles being different).
⚠️ Common Errors
Watch Out!
1. Wrong: Reading ∠ABC as the angle at A Correct: ∠ABC means the angle at vertex B (the middle letter), between BA and BC.
2. Wrong: Confusing line segment AB with length AB — treating AB as a number in an equation without measuring Correct: AB refers to the line segment; AB̄ or |AB| refers to its numerical length. Always clarify which you mean.
3. Wrong: Assuming equal tick marks mean equal angles Correct: Equal tick marks on sides mean equal lengths. Equal arcs at angles mean equal angles. Do not confuse side notation with angle notation.
✍️ 6-Mark Exam Question
Extended Answer
6 marks: In quadrilateral ABCD, AB = CD and BC = AD, but the diagonals are not equal. (a) What type of quadrilateral must ABCD be? (b) If ∠ABC = 110°, find ∠BAD. (c) Explain why the diagonals of this quadrilateral bisect each other.
(a) Since opposite sides are equal, ABCD is a parallelogram.
(b) In a parallelogram, adjacent angles sum to 180°. ∠BAD = 180° − 110° = 70°.
(c) In a parallelogram, opposite sides are equal and parallel. By considering the two triangles formed by diagonal AC, the triangles are congruent (SSS), so the diagonal is bisected at the point of intersection. Similarly for diagonal BD. Therefore both diagonals bisect each other.
Mark scheme: A1 parallelogram, M1 adjacent angles supplementary, A1 70°, M1 congruent triangles argument, A1 bisection, A1 full explanation
📊 AO3: Reason & Interpret
Reasoning and Interpretation
A student draws a triangle with vertices P, Q, R and labels side PQ with 2 tick marks, side QR with 2 tick marks, and side PR with 1 tick mark.
(a) What type of triangle is this?
(b) If ∠PQR = 40°, find the other two angles.
(c) The student then draws another triangle with the same side lengths but in a different orientation. Are the two triangles congruent? Explain.
Answers: (a) Isosceles triangle (PQ = QR). (b) Base angles are equal: ∠QPR = ∠QRP = (180 − 40)/2 = 70° each. (c) Yes — SSS congruence. All three sides are the same length, so the triangles must be congruent regardless of orientation.
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🎬 Video Resources
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