1-4 segments, rays, parallel lines, and planes

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1-4 Segments, Rays, Parallel Lines, and Planes

Objectives:

• Define line segments and rays

• Properly name line segments and rays

• Identify parallel lines and skew lines

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Line Segments

• A line segment is part of a line containing two endpoints and all points between them.

• Unlike lines, which extend forever in both directions, line segments have a definite beginning and end

• A line segment is named with the endpoints

A B

AB or BA

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Rays

• A ray is part of a line that consists of one endpoint and all points of the line extending in one direction

• Name a ray using the endpoint first and then another point on the ray– When naming, make sure the arrow points away from the

endpoint.

A

B

AB , not BA

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Rays, continued

• Are these two rays the same?

A

B

A

B

No• Different endpoints• Extend in different directions

BA

AB

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Opposite Rays

• Are two collinear rays with the same endpoint

• Always form a line

JK

L

KJ and KL are opposite rays

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Parallel Lines

• Lines that– Never intersect– Extend in the same directions– Coplanar

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Skew lines

Lines that:

• Never intersect

• Are noncoplanar

• Extend in different directions

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Parallel Planes

• Parallel planes are planes that never intersect– Example: the purple planes in the above

illustration

• A line and plane that never intersect are also parallel

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Learning Check and Summary• Which of the following has no endpoints?

– Ray, Line Segment, Line• Which of the following has two endpoints?

– Ray, Line Segment, Line• Which of the following has one endpoint and

extends in one direction?– Ray, Line Segment, Line

• Which of the following extend in the same direction?– Parallel lines, skew lines

• Which of the following extend in different directions?– Parallel lines, skew lines

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Exercises

• P. 13-15 All

• P. 253 All

• P. 255 All