Segments, Rays, Parallel Lines and Planes

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1-3 (For help, go to Lesson 1-2.) . 2. 3. . the bottom 5. the top . the front 7. the back . the left side 9. the right side GEOMETRY LESSON 1-3 Segments, Rays, Parallel Lines and Planes ing by appearances, will the lines intersect? me the plane represented by each surface the box.

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Segments, Rays, Parallel Lines and Planes. GEOMETRY LESSON 1-3. (For help, go to Lesson 1-2.). Judging by appearances, will the lines intersect?. 1. 2. 3. 4. the bottom 5. the top 6. the front 7. the back 8. the left side 9. the right side. - PowerPoint PPT Presentation

Transcript of Segments, Rays, Parallel Lines and Planes

Page 1: 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

GEOMETRY LESSON 1-3GEOMETRY LESSON 1-3

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.

Page 2: Segments, Rays, Parallel Lines and Planes

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

GEOMETRY LESSON 1-3GEOMETRY LESSON 1-3

Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes

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Page 3: Segments, Rays, Parallel Lines and Planes

-A part of a line consisting of two endpoints and all points between them.

Line Segment

GEOMETRY LESSON 1-1GEOMETRY LESSON 1-1

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.

Page 4: Segments, Rays, Parallel Lines and Planes

-A part of a line consisting of one endpoint and all points of the line on one side of the endpoint.

Ray

GEOMETRY LESSON 1-1GEOMETRY LESSON 1-1

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.

Page 5: Segments, Rays, Parallel Lines and Planes

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.

GEOMETRY LESSON 1-3GEOMETRY LESSON 1-3

Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes

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Page 6: Segments, Rays, Parallel Lines and Planes

-Coplanar lines that do not intersect

Parallel Lines

GEOMETRY LESSON 1-1GEOMETRY LESSON 1-1

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.

Page 7: Segments, Rays, Parallel Lines and Planes

-Lines that are not coplanar.

Skew Lines

GEOMETRY LESSON 1-1GEOMETRY LESSON 1-1

Patterns and Inductive ReasoningPatterns and Inductive Reasoning

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Definitions

Line a and line b are skew.

Page 8: Segments, Rays, Parallel Lines and Planes

Are the lines below parallel, skew, or neither?

GEOMETRY LESSON 1-1GEOMETRY LESSON 1-1

Patterns and Inductive ReasoningPatterns and Inductive Reasoning

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Think about it!

Page 9: Segments, Rays, Parallel Lines and Planes

Are the lines below parallel, skew, or neither?

GEOMETRY LESSON 1-1GEOMETRY LESSON 1-1

Patterns and Inductive ReasoningPatterns and Inductive Reasoning

1-1

Think about it!

Page 10: Segments, Rays, Parallel Lines and Planes

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.

GEOMETRY LESSON 1-3GEOMETRY LESSON 1-3

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.

Page 11: Segments, Rays, Parallel Lines and Planes

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.

GEOMETRY LESSON 1-3GEOMETRY LESSON 1-3

Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes

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Page 12: Segments, Rays, Parallel Lines and Planes

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

GEOMETRY LESSON 1-3GEOMETRY LESSON 1-3

Segments, Rays, Parallel Lines and PlanesSegments, Rays, Parallel Lines and Planes

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