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: 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 $L$.