Definition:Line/Segment

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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