The building blocks of geometry
All shapes are built from a few simple ideas: points, lines, rays and segments.
Point
A point marks an exact location. It has no size. We draw it as a dot and name it with a capital letter: point A.
Line
A line is perfectly straight and goes on forever in both directions. We draw arrows on both ends. A line is named by any two points on it:
Line AB, written with a double-headed arrow over AB.
Line segment
A line segment is part of a line with two endpoints. It has a definite length you can measure. The sides of a triangle are segments.
Segment AB, written with a bar over AB.
Ray
A ray starts at one endpoint and goes on forever in one direction, like a beam of light from a flashlight or the Sun.
Ray AB starts at A and passes through B. It’s written with a single arrow over AB. The endpoint is always named first: ray AB and ray BA point in opposite directions.
Summary table
| Figure | Endpoints | Length | Drawing | Name |
|---|---|---|---|---|
| Point | — | none | dot | point A |
| Line | 0 | infinite | arrows on both ends | line AB |
| Line segment | 2 | measurable | dots at both ends | segment AB |
| Ray | 1 | infinite in one direction | dot and one arrow | ray AB |
Notation
| Figure | Notation |
|---|---|
| Line | AB with a two-way arrow above |
| Segment | AB with a bar above |
| Ray | AB with a one-way arrow above (pointing right) |
Where we see them
- Edge of a ruler → segment
- Laser beam → ray
- Road painted lines → segments
- Angles → two rays sharing an endpoint (the vertex)
Worked examples
Example 1: A flashlight beam starts at the bulb and shines outward. Which figure is it like?
A ray: one endpoint, endless in one direction.
Example 2: How many endpoints does a line segment have?
Two.
Example 3: Are ray CD and ray DC the same?
No. Ray CD starts at C; ray DC starts at D and points the other way.
Common mistakes
- Drawing a line without arrows: that’s a segment.
- Naming a ray with the endpoint second.
- Thinking a line has a length. Only segments can be measured.
Try it yourself
- Which figure has exactly one endpoint?
- Which figure can be measured with a ruler?
- How do you show that a line goes on forever?
- An angle is made of two ____ with a shared endpoint.
Answers: 1) ray 2) line segment 3) arrows at both ends 4) rays
Quick recap
- A point is a location; a line goes on forever both ways.
- A line segment has two endpoints; a ray has one.
- Use correct notation to name each figure.