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Searching for ## Points and Lines

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Geometry

You will explore the building blocks of Euclidean geometry by studying such things as line segments and points.

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After completing this tutorial, you will be able to complete the following:

- Know the definition of a ray.
- Know that two points determine a ray.

What is a ray?

~ A ray is the set of points that starts at a point on a line and extends infinitely in one direction.

How can we name and represent a ray?

~ A ray is the set of points that starts at a point on a line and extends infinitely in one direction. The starting point is called the endpoint of the ray. We can name a ray by its endpoint and any other point on the ray. For instance, if a ray has endpoint A and B is another point on the line, we call the given ray AB. We represent ray AB by using an arrow over the point names; for example .

What does it mean when we say two rays are equal? What does it mean when we say two rays are opposite rays?

~ Rays with the same endpoint and direction are called equal rays. Rays with the same endpoint and opposite direction are called opposite rays.

List some real-world examples that can be modeled by rays.

~ Answers will vary. It is important to note that rays extend infinitely in one direction, so it is very unlikely that we can find actual physical examples of rays. However, many physical objects can be modeled with rays; some examples include the sun's rays or laser beams.

Why do you think some students might confuse a ray with a line?

~ Answers will vary. Like a line, a ray is infinitely long and has no thickness. However, a ray extends infinitely in only one direction, whereas a line extends infinitely in opposite directions. A ray is the set of points that starts at a point on a line and extends infinitely in one direction, so we may consider a ray as a portion of a line.

Approximate Time | 2 Minutes |

Pre-requisite Concepts | Students should be able to define direction, equal rays, and opposite rays. |

Course | Geometry |

Type of Tutorial | Animation |

Key Vocabulary | direction, equal rays, opposite rays |