Segments, Rays, Parallel Lines and Planes
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Transcript of Segments, Rays, Parallel Lines and Planes
1-3
(For help, go to Lesson 1-2.)
1. 2. 3.
4. the bottom 5. the top
6. the front 7. the back
8. the left side 9. the right side
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Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes
Judging by appearances, will the lines intersect?
Name the plane represented by each surface of the box.
1. no 2. yes 3. yes
4-9. Answers may vary. Samples given:
4. NMR 5. PQL
6. NKL 7. PQR
8. PKN 9. LQR
Solutions
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Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes
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-A part of a line consisting of two endpoints and all points between them.
Line Segment
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Patterns and Inductive ReasoningPatterns and Inductive Reasoning
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Definitions
-Named by the name of the two endpoints with the segment sign above them.
-A part of a line consisting of one endpoint and all points of the line on one side of the endpoint.
Ray
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Patterns and Inductive ReasoningPatterns and Inductive Reasoning
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Definitions
Named by the name of the endpoint and then a second point the ray goes through, with the ray symbol above them.
Name the segments and rays in the figure.
The labeled points in the figure are A, B, and C.
A segment is a part of a line consisting of two endpoints and all points between them. A segment is named by its two endpoints. So the segments are BA (or AB) and BC (or CB).
A ray is a part of a line consisting of one endpoint and all the points of the line on one side of that endpoint. A ray is named by its endpoint first, followed by any other point on the ray. So the rays areBA and BC.
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Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes
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-Coplanar lines that do not intersect
Parallel Lines
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Patterns and Inductive ReasoningPatterns and Inductive Reasoning
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Definitions
-Stated by placing the parallel symbol between the names of the two lines.
-Lines that are not coplanar.
Skew Lines
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Patterns and Inductive ReasoningPatterns and Inductive Reasoning
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Definitions
Line a and line b are skew.
Are the lines below parallel, skew, or neither?
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Think about it!
Are the lines below parallel, skew, or neither?
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Think about it!
Use the figure below. Name all segments that
are parallel to AE. Name all segments that are skew to AE.
Parallel segments lie in the same plane, and the lines that contain them do not intersect. The three segments in the figure above that are parallel to AE are BF, CG, and DH.
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Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes
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Skew lines are lines that do not lie in the same plane. The four lines in the figure that do not lie in the same plane as AE are BC, CD, FG, and GH.
Planes are parallel if they do not intersect. If the walls of your classroom are vertical, opposite walls are parts of parallel planes. If the ceiling and floor of the classroom are level, they are parts of parallel planes.
Identify a pair of parallel planes in your classroom.
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Use the figure below for Exercises 1-3.
1. Name the segments that form the triangle. 2. Name the rays that have point T as their endpoint.
3. Explain how you can tell that no lines in the figure are parallel or skew.
Use the figure below for Exercises 4 and 5.
4. Name a pair of parallel planes.
5. Name a line that is skew to XW.
TO, TP, TR, TS
The three pairs of lines intersect, so they cannot be parallel or skew.
AC or BD
RS, TR, ST plane BCD || plane XWQ
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Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes
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