# Difference Between Line and Line Segment – Definition, Examples

## What Is the Difference Between a Line and a Line Segment?

The difference between a line and a line segment is that a line segment has two endpoints (has a finite length), whereas a line does not have endpoints (extends infinitely in both directions).

A line is a basic and simple shape in geometry. Look around, and you can see lines in different shapes and everyday objects! Every shape that we study in geometry is made by joining a number of lines.

A line can be extended infinitely in the opposite directions. A line segment is part of a line, and has two definite endpoints. It has length, but it does not have a width and depth.

## Definition of Line

A line is defined as a straight one-dimensional geometric shape that does not have a thickness, and it extends endlessly in both directions.

A line has infinite length. We show it by drawing arrows at both ends. A line can be named by any two points lying on the line. We can also name a line using a single lowercase letter.

Take a look at the picture given below.

The notation for line AB is Here, we have a line m.

## Definition of Line Segment

A line segment is defined as a section of a line bounded by two points or connecting two points. It is the shortest distance between two points that can be measured.

The notation of a line segment is given by two endpoints with the bar symbol $( \overline{} )$ on top.

If a line segment has endpoints P and Q, it can be written as $\overline{PQ}$. Note that line segment PQ is the same as line segment QP.

## How Is a Line Different from a Line Segment?

The key difference between a line and a line segment is that a line is extended in both directions infinitely. It has infinite length. We show it by drawing arrows on both sides. However, a line segment has two defined endpoints, thereby a definite length.

## Facts about the Difference between Line Segment and Line

• Euclid, a Greek mathematician—fondly known as the Father of Geometry—introduced the concept of a line. He defined it as “a breadthless length.”
• A ray is a geometric figure that has a starting point but no endpoint. It extends infinitely in one direction.
• A set of three or more points are called collinear points if they lie on the same line.
• Only one line can pass through two given points.
• A line and a line segment are one-dimensional shapes.

## Conclusion

In this article, we have learned about the definition of a line and a line segment and the differences between them. Let’s solve some examples to understand the concept better.

## Solved Examples on Difference Between Line Segment and Line

1.  Which of the following diagrams is a line segment ?

Solution:

Diagram i) is a line segment as it has 2 definite endpoints.

Diagram ii) is a line as it extends endlessly in both the directions.

Diagram iii) is a ray since it has a starting point but no endpoint.

Diagram iv) is a point.

2. Name the following figures.

(a)                                                            (b)

Solution:

The figure (a) is a line segment. It is represented as AB.

The figure (b) is a line with points A and B lying on it. Line AB is denoted as .

3. Write all the possible line segments in the given figure.

Solution:

Here, we can find all the possible line segments by taking any two endpoints.

Line segment AB: AB

Line segment BC: BC

Line segment CD: CD

Line segment BD: BD

Line segment AC: AC

4. Write whether the following statements are correct or incorrect. Correct the incorrect ones.

A. A line segment has one endpoint.

B. A line is a part of the line segment.

C. A line segment has a fixed length.

Solution:

A. A line segment has one endpoint.

The given statement is incorrect.

A line segment has two endpoints.

B. A line is a part of the line segment.

The given statement is incorrect.

A line segment is a part of the line.

C. A line segment has a fixed length.

The given statement is correct.

## Practice Problems on Difference Between Line Segment and Line

1

### A one-dimensional figure, which has length, but no width is called ________.

A ray
A line segment
A line
None of the above.
CorrectIncorrect
A one-dimensional figure, which has length but no width is called a line.
2

### ________ can be extended in both directions infinitely.

A ray
A line
A line segment
A point
CorrectIncorrect
A line can be extended infinitely in both ends towards the opposite directions.
3

### Identify the name of the red part in the given figure. Ray AB
Line AB
Line segment AB
Line BA
CorrectIncorrect
Correct answer is: Line segment AB
A line segment is a section of a line formed by connecting two distinct points. Here, the red section is a part of the blue line. It connects two points, A and B.
4

### Which of these notations represent a line segment?

$\overline{PQ}$
$\widehat{XY}$
$|CD|$
$\overleftrightarrow{\rm AB}$
CorrectIncorrect
Correct answer is: $\overline{PQ}$
A line segment is usually represented by the bar symbol $(\overline{ })$ on top of the endpoints. Say, a line segment has endpoints P and Q, it can be denoted as $\overline{PQ}$.
5

### Which of the following is NOT TRUE ?

The length of a line cannot be measured.
A line does not have width or thickness.
A line extends endlessly in both directions.
A line is a two-dimensional figure.
CorrectIncorrect
Correct answer is: The length of a line cannot be measured.
In geometry, a line is a one-dimensional figure.

## Frequently Asked Questions on the Difference Between Line Segment and Line

A ray is a part of a line that has a fixed starting point but no endpoint. It can extend infinitely in one direction. Since a ray has no endpoint, we can’t measure its length.

A ray is denoted by drawing a small ray on top of the name of the ray.

Collinear means lying on the same line. Three or more points are said to be collinear if they lie on a single straight line.

A line consists of an infinite number of points.

We may find various examples of line segments surrounding us, such as the edge of tiles, the edges of rulers, the edge of a rectangular table, the edge of a book, etc.

Yes, both notations denote the same line since a line extends infinitely on both sides.

Line segments PQ and QP represent the same segment since the endpoints are the same.