Let us think, what is a segment in mathematics? A part of a geometrical figure cut off by one or more points, lines, such as the finite part of the line between two points in a line referred to as a segment. Mark two points A and B on a line and pick this segment separately, it becomes a **line segment**. A line segment has two definite endpoints in a line. The length of the line segment is non-changeable. So, a line segment is a piece of a line having two endpoints.

## Units for Measuring the length of a line segment-

The length can be measured by metric units such as centimeters (cm), millimeters (mm), or in units like feet or inches.

## Representation of line segment-

- A line segment with two endpoints (a closed line segment) A and B. It is denoted by the bar symbol (—) such as AB.
- An open line segment is usually represented by (↔) which doesn’t have any end.
- A half-open line segment is represented by a ray with a right arrow (→) which only have a starting point

## Types of line segments-

3 types of line segments are their-

(i) A closed line segment- Line segment consists of both endpoints.

(ii) An open line segment- Line segment extended to infinity on either side.

(iii) Half-open line segment- A line segment that has exactly one endpoint is called a half-open line segment.

## Examples of Line Segments

In 2-D geometry, the most common examples are the polygons, which are made up of line segments.

- A triangle is drawn up by three line segments.
- A square is made up of four-line segments.

Line Segment Formula

As we know, a line segment has two endpoints. Now, if we all know the coordinates of the endpoints, then we can calculate the length of the road segment by distance formula.

D= √(x2−x1)^{2}+(y2−y1)^{2}

Suppose a line segment has coordinates (-5, 5) and (–2, –7). Find the length of line segment.

Therefore, by distance formula,

D= √(-5-5)^{2} + (-7+2)^{2}

√(-10)^{2} + (-5)^{2} = √100 +25 = √125

There are many methods of measuring line segment-

(i) By observation.

(ii) With the help of trace paper.

(iii) With the help of a ruler and divider.

## Construction of line segments

Let us learn about the construction of line segments. To draw a line segment, we need a compass and measuring ruler or scale.

- Let us assume we need to draw a line segment of length 4cm. Then follow the below-given steps:
- Draw a line of any length.
- Mark a starting point P on the line.
- Now using a scale or ruler, locate the pointer of the compass 4cm apart from the pencil’s lead.
- Again, place the compass at point P on the line. And mark an arc with the same measurement.
- Now, mark this point as Q.

Hence, PQ is the required line segment of length 4cm.

## Some important properties of a line segment-

· A line has indefinite ends and cannot be measured (open line segment).

· A line segment has a start point and an endpoint, thus, it can be measured (closed line segments).

· Line segments have a defined length. Hence, they form the sides of any polygon (like- triangle, square, etc.)

· A ray has just one start point and no endpoint. Therefore, it cannot be measured (half-one ended segment)

· If you want to understand the concept of rays, take an example of sun rays which have a beginning point but no endpoint.

There is also a concept of **parallel lines**, perpendicular lines, intersecting lines, non-intersecting lines. To learn different types of concepts use Cuemath, which is an online platform to learn mathematics easily. This platform provides the right direction to every student. Anyone can learn difficult problems with the help of this online platform under the guidance of expert teachers.