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Lines, Segments, and Rays

Most students of mathematics have an intuitive understanding of what a line is, but a good definition can be difficult to write. Likewise, lines are related to line segments and rays, both of which are also explored in this article. Let's get started!

Lines, segments, and rays: lines

We can say that a line is an infinitely thin, infinitely long collection of points extending in two opposite directions. Since we cannot actually draw lines of infinite length in geometry, we use arrows to indicate that they stretch on in both directions:

There are two different ways to name lines. If we have the names of at least two points on the line, we can name it after them. For example, the line on the left above could be called line AB. If we don't, we can use a lowercase letter such as line m on the right.

Lines, segments, and rays: line segments

A line segment is like a line except that it has two clearly defined endpoints, meaning that it isn't infinitely long. That means that we can measure the length of a line segment whereas we cannot measure the length of a line. Here is an example:

Line segments are always named after their endpoints. For example, the segment above would be called segment AB.

Lines, segments, and rays: rays

A ray is part of a line with a clear endpoint in one direction that stretches indefinitely in the other. Since one side is infinitely long, we cannot measure the length of a ray. The diagram below illustrates what a ray looks like:

Rays are named by their endpoints first and any other named point after that. For example, the ray above would be named BA because B is the endpoint and A is a named point on the ray.

Practice questions on lines, rays, and segments

a. Write two different names for the ray highlighted in red in the diagram below:

Rays are named after their endpoint followed by any other named points on the ray. In the diagram above, point C is the endpoint so both names have to start with that. The ray also includes point E and point F, so it could be named CE or CF.

b. In your own words, explain the difference between lines, line segments, and rays.

Lines have no set endpoints, line segments have endpoints in both directions, and rays have one endpoint then continue off in one direction.

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