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Opposite Rays in Geometry: Definition & Example

Opposite Rays in Geometry: Definition & Example
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  • 0:04 Definition of Opposite Rays
  • 1:35 Examples of Opposite Rays
  • 2:43 Lesson Summary
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Lesson Transcript
Instructor: Miriam Snare

Miriam has taught middle- and high-school math for over 10 years and has a master's degree in Curriculum and Instruction.

This lesson will teach you the definition of opposite rays. You will be given a couple of examples. Then, you will be able to test yourself with a quiz.

Opposite Rays - Definition

A ray in geometry is half of a line. A ray has'one endpoint and extends indefinitely in one direction. Think about a ray of light from a star: The star is the endpoint and the ray of light can travel through the whole universe (if nothing gets in the way).

Ray

A pair of opposite rays are two rays that have the 'same endpoint and extend in opposite directions. So, together a pair of opposite rays always forms a straight line.

You can use a pencil as a real-world example of opposite rays. Hold a pencil between your thumb and index finger somewhere near the middle of the pencil, like this:

Finger holding a pencil

Extending away from your finger, there are now two opposite rays along the pencil. One ray extends from your finger through the sharpened end of the pencil. The other ray extends from your finger through the eraser.

Let's turn the pencil picture into a geometry figure, so we can look at how to name the opposite rays. We are going to draw a line along the pencil. We are going to label the sharpened end of the pencil as point P, the point where your finger is as point F, and the point where the eraser is as point E.

Line with points

Remember that rays are always named with two points, the first point in the name must be the endpoint. So, when you name opposite rays, the first letter in the name of both rays must be the same. Therefore, the opposite rays along our pencil are ray FP and ray FE.

Hint: The three points involved in naming a pair of opposite rays must always lie in one straight line.

Examples of Opposite Rays

Let's look at a couple of examples that use opposite rays.

Can you name a pair of opposite rays in the diagram shown here?

Diagram of several rays

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