Line Segment

In geometry, a line segment is bounded by two distinct points on a line. Or we can say a line segment is part of the line that connects to points. A line has no endpoints and extends infinitely in both the direction but a line segment has two fixed or definite endpoints. Line segment and a ray have a difference that a ray has only one endpoint, which is its starting point.

Most of the shapes that we see around us are either made up of lines or curves. Various geometrical shapes are a combination of these. A one-dimensional collection of points extending infinitely in either direction is a line and any portion of a line which has two endpoints is a line segment.

The above figure represents a line segment with two endpoints A and B and is denoted by the bar symbol (—) such as \(\overline{AB}\). The length of a line segment can be varying and various methods are adopted to measure its length. To compare two or more line segments, a relationship between their lengths is established. Let us discuss these methods one by one.

Line Segment Definition

A line segment has two endpoints in a line. The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimetre (cm), millimetres (mm) or by conventional units like feet or inches.

A closed line segment consists of both endpoints, whereas an open line segment are exclusive of the two endpoints. A line segment which has exactly one endpoint is called half-open line segment.

Measuring Line Segment

By Observation

The most trivial method of comparison of two line segments is simple observation. Just by observing two line segments one can predict which is long or short compared to the other.

In the above figure, by observation itself, we can say that the line segment CD is greater in length as compared to the line segment AB. But this method has several constraints, every time we cannot rely simply on observation to compare two line segments.

Using Trace Paper

With the help of trace paper, two line segments can be easily compared. Trace one line segment and place it over on the other segment and it can be easily deduced which is greater in length. For more than two line segments repeat the process again and again.

For precise comparison, the line segments must be traced accurately. Hence this method depends on the accuracy of tracing which puts a limitation on this method.

Using Ruler and Divider

There are certain markings on the ruler beginning from zero as shown in the fig. given below, these markings divide the ruler into equal parts. Each part is equal to a length of 1 cm and these unit centimetres are further subdivided into 10 parts and each sub-part is equivalent to 1 millimetre.

To measure a line segment AB, place the zero marking of the ruler along the beginning of the line and measure its length accordingly.

In the figure given above, the length of line segment AB is 8 cm.

To eliminate the positioning error we use a divider. Place one of the needles of the divider at A and other at B and then place the divider along the ruler and measure its length. This method is more accurate and reliable.

Construction of Line Segment

Here we will learn to draw a line segment with the help of a compass and measuring ruler or scale.

  • Let us assume, we need to draw a line segment of length 7cm. Then follow the below-given steps:
  • Draw a line of any length without a measurement (keeping in consideration of the length of the line segment)
  • Mark a point P on the line, which will be the starting point of the line segment.
  • Now using a scale or ruler, locate the pointer of compass 7cm apart from the pencil’s lead.
  • Again, place the pointer of the compass at point P on the line and with the same measurement mark an arc with the pencil.
  • Now, mark this point as Q

Hence, PQ is the required line segment of length 7 cm.