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Mom's Basement University

Line Segments and Rays

What You’ll Learn

Section titled “What You’ll Learn”

In this lesson you’ll learn the differences between lines, line segments, and rays, and how to name and use them.

The Concept

Section titled “The Concept”

  • Line: Extends infinitely in both directions. Named with two points (line AB) or a single lowercase letter. Written as AB↔\overleftrightarrow{AB}.

  • Line segment: A finite portion of a line with two endpoints. Named with its two endpoints (segment AB). Written as AB‾\overline{AB}.

  • Ray: Starts at one endpoint and extends infinitely in one direction. Named with the endpoint first, then another point on the ray (ray AB). Written as AB→\overrightarrow{AB}.

Line Extends forever both ways Symbol: ↔ Line Segment A B Two endpoints, finite length Symbol: — Ray C D One endpoint, extends forever Symbol: →

Important notes:

  • A line segment has a definite length.
  • A ray has one endpoint and goes on forever in one direction.
  • Two rays with the same endpoint but going in opposite directions form a line.

Worked Example

Section titled “Worked Example”

  1. Name the figure with endpoints A and B that has a definite length.

    Line segment AB, written AB‾\overline{AB}

  2. Name the figure that starts at point C and goes through point D forever.

    Ray CD, written CD→\overrightarrow{CD}

  3. How many endpoints does a line have?

    Zero. It extends forever both ways.

Real-World Application

Section titled “Real-World Application”
  • Line segment: The edge of a table, a piece of lumber you cut to length, the distance between two cities on a map.
  • Ray: A beam of light from a flashlight, a laser pointer, the path of a train track going off into the distance.
  • Line: The horizon, a straight road that seems to go on forever, the path of a laser in theory.

These ideas help with construction, design, navigation, and understanding diagrams or blueprints.

Quiz

Section titled “Quiz”
Which figure has exactly two endpoints?
A figure starts at point A and goes through point B forever in one direction. What is it?
How many endpoints does a line have?
Which notation represents a line segment between A and B?
Two rays that share the same endpoint form a: