What Are the Subsets of a Line in Geometry?

In geometry, a shape consists of a connection of planes, and any plane consists of a connection

of lines. You can then break down lines into two further subsets --- line segments and rays. By

learning about the line and its subsets, you will develop a better understanding of the

mathematics of geometry.

Importance of Lines

Lines are important figures to all areas of mathematics. In geometry, a line is the area

where two planes come together. One of the most important aspects of a line is that it

extends from either side to infinity. To make these objects easier to work with,

mathematicians break them down into subsets.

Subsets Defined

Subsets are an important part of mathematics in general, but they are especially important

to geometry. In mathematics, a subset is a piece of something larger. For example, a

piece of pie is a subset of the entire pie. Geometry deals specifically with shapes, making

subsets an important idea to the field. Mathematicians use subsets to simplify complex

problems by investigating the smaller parts of the problem one by one and connecting the

pieces to determine a solution.

Subset of Rays

A ray is a part of a line that starts at one point and extends infinitely in a set direction. A

ray is different from a line because it has a starting point or origin, and extends infinitely

from there. In contrast, a line extends infinitely in two opposite directions. So a ray that

starts on a line and continues in one direction on the line is a subset of the line.

Subset of Line Segments

A line segment begins at one point and ends at another. They are important because they make

the mathematics of lines more manageable. Unlike a ray or a line, line segments are finite; they

do not stretch to infinity in either direction. Line segments that share the starting point, ending

point and all points in the middle with a given line make up a subset of that line.