Geometry Points, Lines and Planes

1. Geometry Points, Lines and Planes

4. Geometry 9 • Title: Points, lines and Planes

5. Undefined Terms Words that do not have formal definitions but there is an agreement about what they mean.

6. Point

7. Line

8. Plane

9. Collinear Points

10. Coplanar Points

11. Defined Terms Terms that can be described using known terms like Point or Line

12. Segment

13. Ray

14. Opposite Ray

15. Intersection

16. a. Are points S, P, T collinear? Is so name the line they line on. b. Name four points that are coplanar. • yes, line m. (ST) EXAMPLE 1 Name points, lines, and planes SOLUTION 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.

17. EXAMPLE 1 Name points, lines, and planes

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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.

24. ANSWER Linek Use the diagram at the right. 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.

25. Homework • Pg 19 1-5, 11-16