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Mastering Points, Lines, and Planes Theory

Learn the fundamentals of points, lines, and planes in geometry with clear explanations and examples. Understand concepts like collinearity, coplanarity, and segments to enhance your understanding. Perfect for high school students.

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Mastering Points, Lines, and Planes Theory

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  1. Points, Lines and Planes Thanks Mrs. Nicole Takayama Smyrna High School

  2. Point • Has no dimension • Represented by a small dot • Named by a capital print letter • No symbol

  3. A Example SayWrite A “ Point A”

  4. Line • Has one dimension • Extends without end in two directions • Represented by a line with 2 arrowheads • Named by 2 points or a lowercase, script letter • Symbol

  5. Example SayWrite AB BA BC CB AC CA d d “line AB” “line BA” “line BC” “line CB” “line AC” \ “line CA” “line d” C B A

  6. Collinear Points • Points on the same line

  7. Example SayWrite A, B, and C are collinear. They are all on d d “points A, B, and C are collinear. They are all on line d.” C B A

  8. Noncollinear Points • Points not on the same line

  9. Example SayWrite d A, B, and C are noncollinear. A & B are on d, but C is not. “points A, B, and C are noncollinear. Points A and B are on line d, but point C is not.” C B A

  10. Plane • Has 2 dimensions • Flat surface that extends without end • Represented by a parallelogram • Named by three noncollinear points or capital, script letter • No symbol

  11. Example SayWrite ABC P “plane ABC” “plane P” P C B A

  12. Coplanar • On the same plane • Lines can be coplanar • Points can be coplanar

  13. Example SayWrite A, B, & C are coplanar, they lie on P “Points A, B, and C are coplanar. They lie on plane P.” P C B A

  14. Noncoplanar • NOT on the same plane

  15. Example SayWrite BC and AD are noncoplanar “Lines AD and BC are noncoplanar. Line BC lies on plane ABC, while line AD passes through it. P C B A D

  16. Segment • Part of a line • Has a beginning and an end (both are called endpoints) • Named by the two endpoints • Symbol

  17. Example SayWrite AC CA “segment AC” “segment CA” C A

  18. Ray • Part of a line • Has a beginning (called an endpoint) and continues forever in ONE direction • Named by the endpoint and one other point to show direction • Symbol

  19. Example SayWrite AB AC “ray AB” “ray AC” C B A

  20. Homework Complete the following worksheets Tutor side Problems 1 – 10 skip #8 Points, Lines and Segments side 1-15

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