Points, Lines, and Planes

# Points, Lines, and Planes

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## Points, Lines, and Planes

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1. HE Points, Lines, and Planes GEOMETRY LESSON 1-3 Use the diagram at right. 1. Name three collinear points. 2. Name two different planes that contain points C and G. 3. Name the intersection of plane AED and plane HEG. 4. How many planes contain the points A, F, and H? 5. Show that this conjecture is false by finding one counterexample: Two planes always intersect in exactly one line. D, J, and H planes BCGF and CGHD 1 Sample: Planes AEHD and BFGC never intersect. 1-3

2. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-4 (For help, go to Lesson 1-3.) 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 2. yes 1. no 3. no Name the plane represented by each surface   of the box. 4-9. Answers may vary. Samples given: 5.PQL 4.NMR 6.NKL 7.PQR 9.LQR 8.PKN Check Skills You’ll Need 1-4

3. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-4 Definitions 1-4

4. Name the segments and rays in the figure. 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 are BA and BC. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-4 Quick Check The labeled points in the figure areA,B,and C. 1-4

5. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-4 Definitions 1-4

6. 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. 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. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-4 Quick Check 1-4

7. Identify a pair of parallel planes in your classroom. Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-4 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. Quick Check 1-4

8. RS, TR, ST TO, TP, TR, TS AC or BD Segments, Rays, Parallel Lines and Planes GEOMETRY LESSON 1-4 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. 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. plane ABCD || plane XWQ The three pairs of lines intersect, so they cannot be parallel or skew. 1-4