What Are the Subsets of a Line in Geometry?

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Lines are important to all fields of mathematics.

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.

  1. 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

    • Line segments are small pieces of a larger line.
      Line segments are small pieces of a larger line.

      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.

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