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Graphing Inequalities and Geometric Definitions

Learn about graphing inequalities on a number line and definitions of points, lines, and planes. Identify collinear and coplanar points and name segments, rays, and opposite rays.

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Graphing Inequalities and Geometric Definitions

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  1. Warm up • Graph the inequality x ≤ 1 on a number line.

  2. Definitions Point – no dimension. Represented by a dot

  3. Line – one dimensional. A line with two arrowheads Through any two points, there is exactly one line and can be named with the two points.

  4. Plane – has two dimensions. Extends with no boundaries. Use three points to name. Through any three non-colinear point exists exactly one plane.

  5. Definitions Collinear Points – points that lie on the same line. Coplanar points – points that lie on the same plane.

  6. 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

  7. 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.

  8. 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

  9. Definitions Line Segment – The line segment AB (AB) consists of the endpoints A and B and all points on line AB that are between A and B.

  10. Definitions Ray– The ray AB (AB) consists of the endpoint A and B and all points on line AB lie on the same side as B. Opposite Rays – same endpoint, and together make a line.

  11. 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

  12. 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

  13. Homework: Page 5: 1, 3-11, 17-22

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