# Definition:Line/Segment

Jump to navigation
Jump to search

## Definition

A **line segment** is any line (straight or not) which terminates at two points.

### Straight Line Segment

A **straight line segment** is a line segment which is straight.

In the words of Euclid:

*A straight line segment can be drawn joining any two points.*

(*The Elements*: Postulates: Euclid's Second Postulate)

### Endpoint

Each of the points at either end of a line segment is called an **endpoint** of that line segment.

Similarly, the point at which an infinite half-line terminates is called **the endpoint** of that line.

In the words of Euclid:

*The extremities of a line are points.*

(*The Elements*: Book $\text{I}$: Definition $3$)

### Midpoint

Let $L = AB$ be a line segment whose endpoints are $A$ and $B$.

Let $M$ be a point on $L$ such that the line segment $AM$ is equal to the line segment $MB$.

Then $M$ is the **midpoint** of $L$.