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Chapter 1

Chapter 1. Section 1.1 Identify Points, Lines, and Planes. Warm Up Problems. Solve the inequality. Graph the solution. To define it or not to define it. Definition : Using known words to define a new word Undefined terms: When a term is not given a definition

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Chapter 1

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  1. Chapter 1 Section 1.1 Identify Points, Lines, and Planes

  2. Warm Up Problems Solve the inequality. Graph the solution.

  3. To define it or not to define it • Definition: Using known words to define a new word • Undefined terms: When a term is not given a definition • Points, Lines, and Planes are all undefined terms • No formal definitions, but there is agreement about what they mean

  4. Undefined terms • Point • Something with no dimension • Line • Something that extends forever in one dimension • Plane • Something that extends forever in two dimensions •

  5. Points • Points do not have actual size. • How to Sketch: Using dots • How to label: Use capital letters Never name two points with the same letter (in the same sketch). A B A C

  6. Lines • Lines extend indefinitely and have no thickness or width. • How to sketch : using arrows at both ends. • How to name: 2 ways (1) small script letter – line n (2) any two points on the line - • Never name a line using three points - n A B C

  7. Planes • A plane is a flat surface that extends indefinitely in all directions. • How to sketch: Use a parallelogram (four sided figure) • How to name: 2 ways (1) Capital script letter – Plane M (2) Any 3 non collinear points in the plane - Plane: ABC/ ACB / BAC / BCA / CAB / CBA A M B C Horizontal Plane Vertical Plane Other

  8. a. Give two other names for PQand for plane R. b.Name three points that are collinear. Name four points that are coplanar. • Other names for PQare QPand line n. Other names for plane Rare plane SVT and plane PTV. EXAMPLE 1 Name points, lines, and planes SOLUTION

  9. EXAMPLE 1 Name points, lines, and planes b. Points S, P, and Tlie on the same line, so they are collinear. Points S, P, T,and Vlie in the same plane, so they are coplanar.

  10. 1. Use the diagram in Example 1. Give two other names for ST. Name a point that is not coplanar with points Q, S, and T. ANSWER TS, PT; point V for Example 1 GUIDED PRACTICE

  11. Defined Terms • Collinear Points • Points that lie on the same line • Coplanar Points • Points that lie in the same plane • Intersect • Two or more geometric figures are said to intersect if they have one or more points in common • Intersection • Set of points the figures have in common

  12. Defined Terms • Line Segment • A piece of a line cut off by two end points • Ray • All the points on one side of a given point called the endpoint or initial point End Point

  13. • • B A • B A Symbolization Use two points on the line and draw a line above them Lines Rays Use the end point and any other point on the ray then draw a ray on top Opposite Rays: Two rays that have the same end point but extend in opposite directions

  14. a. Give another name for GH . a. Another name for GHis HG . b. The rays with endpoint Jare JE, JG, JF, and JH . The pairs of opposite rays with endpoint Jare JEand JF, and JGand JH. EXAMPLE 2 Name segments, rays, and opposite rays b. Name all rays with endpoint J . Which of these rays are opposite rays? SOLUTION

  15. 2. Give another name for EF ANSWER FE 3. Are HJand JH the same ray ? Are HJand HGthe same ray? Explain. ANSWER No; the rays have different endpoints.Yes; points J and G lie on the same side of H. for Example 2 GUIDED PRACTICE

  16. Intersection of Figures The intersection of two figures is the set of points that are common in both figures. The intersection of two lines is a point. m Line m and line n intersect at point P. P n Continued…….

  17. 3 Possibilities of Intersection of a Line and a Plane (1) Line passes through plane – intersection is a point. (2) Line lies on the plane - intersection is a line. (3) Line is parallel to the plane - no common points.

  18. Intersection of Two Planes is a Line. B P A R Plane P and Plane R intersect at the line

  19. c. a. b. EXAMPLE 3 Sketch intersections of lines and planes a. Sketch a plane and a line that is in the plane. b.Sketch a plane and a line that does not intersect the plane. c. Sketch a plane and a line that intersects the plane at a point. SOLUTION

  20. STEP 1 Draw: a vertical plane. Shade the plane. STEP 2 Draw: a second plane that is horizontal. Shade this plane a different color. Use dashed lines to show where one plane is hidden. STEP 3 Draw: the line of intersection. EXAMPLE 4 Sketch intersections of planes Sketch two planes that intersect in a line. SOLUTION

  21. ANSWER Use the diagram at the right. 5. Name the intersection of PQand line k. ANSWER Point M for Examples 3 and 4 GUIDED PRACTICE • Sketch two different lines that intersect a plane at the same point.

  22. ANSWER Linek ANSWER Linek for Examples 3 and 4 GUIDED PRACTICE 6. Name the intersection of plane A and plane B. 7. Name the intersection of line kand plane A.

  23. HW #1 p. 876: 1-6p. 5-8: 1-16, 17-27 odd, 40-44, 47, 50, 53, 56

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