# What is a Line Segment in Geometry? - Definition, Formula & Example

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Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

Line segments are essential elements to many geometric concepts. In this lesson you will explore line segments in geometry, learn the formula for finding the length of a line segment, review what you've learned with some examples, and test your understanding with a short quiz.

## Definition of a Line Segment

A line segment is a piece, or part, of a line in geometry. A line segment is represented by end points on each end of the line segment. A line in geometry is represented by a line with arrows at each end. A line segment and a line are different because a line goes on forever while a line segment has a distinct beginning and end.

You can imagine a map with blocks of houses in a neighborhood when thinking of a line segment. When walking from your house to a friend's house you will start at a point and end at a point. The distance between your house and your friend's house can be represented by a black line segment.

In geometry, you will write a line segment using the letters for each of the end points and a line over the top of the letters. For example, if your end points were A and B, then you would write your line segment AB with a line over the top.

## Formula for Finding the Length of a Line Segment

When you want to find the length of a line segment, you will need to create an equation based on the information given to you in the problem. It is possible to use the measurements for two line segments to find the length of the third line segment. What is the length of line segment AC?

The equation would be:

line segment AB + line segment BC = line segment AC
5 + 3 = 8

The length of line segment AC is 8.

## Line Segment on a Cartesian Plane

Line segments are also seen on graphs or the Cartesian plane. You can find the length of a line segment by counting the units that the line segment covers. Counting the units on a graph is like counting the number of blocks traveled between your house and your friend's house.

Count the number of units between the two end points. On this particular graph, the line segment has a length of 5 units.

## Formula for the Pythagorean Theorem

You can find the length of a diagonal line by using the Pythagorean theorem.

When finding the length of a line segment in a right triangle you can use the Pythagorean theorem: A squared plus B squared equals C squared.

In this example, when looking for the length of line segment ST you can use the length of line segments TU and SU.

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