Definition:Line/Segment
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: Book $\text{I}$: Postulates: Euclid's First 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 $MB$.
That is, let $M$ be the bisector of $L$.
Then $M$ is the midpoint of $L$.
Equality of Line Segments
Two line segments are equal if and only if they have the same length.
Also known as
A line segment is also known as just a segment.
However, the word segment has a number of different meanings, so the full term line segment is preferred on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Also see
- Results about line segments can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): segment: 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): segment: 1.