Exercise Solutions Available
Step-by-step answers for all textbook questions in this chapter
Point, Line, Line Segment, Ray
Point
- A point is a location in space — it has no size, shape, or dimension.
- Represented by a dot and named with a capital letter: point A (•A)
Line
- Extends infinitely in both directions.
- Has no endpoints.
- Written as: ↔AB (with arrows on both ends)
- Infinite number of points lie on a line.
Line Segment
- Part of a line with two endpoints.
- Has a definite, measurable length.
- Written as: AB (with bar on top)
Ray
- Starts at one point and extends infinitely in one direction.
- Has one endpoint (starting point).
- Written as: →AB (arrow on one end)
| Figure | Endpoints | Length | Direction |
|---|---|---|---|
| Line | 0 | Infinite | Both ways |
| Line segment | 2 | Fixed | — |
| Ray | 1 | Infinite | One way |
Intersecting and Parallel Lines
Intersecting lines: Two lines that meet at a point. That point is called the point of intersection.
Parallel lines: Two lines in the same plane that never meet, no matter how far extended. They are always the same distance apart.
Angles
An angle is formed by two rays (arms) meeting at a common point called the vertex.
- Written as: ∠ABC (B is the vertex)
- Measured in degrees (°)
Parts of an Angle
- Vertex — the common endpoint
- Arms — the two rays forming the angle
- Interior — region inside the angle
- Exterior — region outside the angle
Triangles
A triangle is a polygon with 3 sides and 3 angles.
- A triangle ABC has:
- Vertices: A, B, C
- Sides: AB, BC, CA
- Angles: ∠A, ∠B, ∠C
- Interior: region enclosed inside
- Exterior: region outside
Quadrilaterals
A quadrilateral is a polygon with 4 sides, 4 angles, and 4 vertices.
- A quadrilateral ABCD has:
- 4 sides: AB, BC, CD, DA
- 4 angles: ∠A, ∠B, ∠C, ∠D
- 2 diagonals: AC and BD (line segments joining opposite vertices)
- Adjacent sides share a vertex; opposite sides don't share a vertex.
Circles
A circle is the collection of all points equidistant from a fixed centre point.
Parts of a Circle
| Part | Definition |
|---|---|
| Centre (O) | Fixed point equidistant from all points on the circle |
| Radius (r) | Line segment from centre to any point on circle |
| Diameter (d) | Chord passing through centre; d = 2r (longest chord) |
| Chord | Line segment joining any two points on the circle |
| Arc | Part of the circle between two points |
| Semicircle | Half the circle (diameter divides circle into 2 semicircles) |
| Sector | Region bounded by two radii and an arc (like a slice of pie) |
Key: Diameter = 2 × Radius; Radius = Diameter ÷ 2
Curves
Curve: Any drawing made without lifting the pencil.
| Type | Description |
|---|---|
| Simple curve | Does not cross itself |
| Open curve | Ends are different points |
| Closed curve | Ends meet at the same point |
| Polygon | Closed curve made entirely of line segments |
Key Vocabulary
| Term | Meaning |
|---|---|
| Point | Location, no dimension |
| Line | Infinite in both directions |
| Line segment | Fixed length, two endpoints |
| Ray | One endpoint, infinite in one direction |
| Angle | Two rays meeting at a vertex |
| Vertex | Corner point; meeting point of arms |
| Polygon | Closed figure with straight sides |
| Chord | Line segment joining two points on a circle |
| Diameter | Longest chord through centre |
| Radius | Centre to circle, half of diameter |
Exam Tips
- Line, line segment, ray — differences are asked in 1-mark questions; use proper notation with arrows.
- Diameter = 2 × Radius — always.
- In a triangle: 3 sides, 3 angles, 3 vertices.
- In a quadrilateral: 4 sides, 4 angles, 4 vertices, 2 diagonals.
- A chord that passes through the centre is the diameter — it is the longest possible chord.
- Learn to identify interior/exterior of angles and polygons from diagrams.
Frequently Asked Questions
A line extends infinitely in both directions — no endpoints. A line segment has two endpoints and a fixed length. A ray has one starting point (endpoint) and extends infinitely in one direction only.