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Geometry Basics

Geometry Basics. Sections covered: 1.3 Points, Lines, & Planes 1.4 Segments, Rays, Parallel Lines, & Planes. Space. the set of all points. Points. location in space with no size, represented by a small dot and a letter. Line.

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Geometry Basics

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  1. Geometry Basics Sections covered: 1.3 Points, Lines, & Planes 1.4 Segments, Rays, Parallel Lines, & Planes

  2. Space • the set of all points

  3. Points • location in space with no size, represented by a small dot and a letter

  4. Line • series of points that extends in two opposite directions without end • Named:

  5. Collinear Points • points that lie on the same line

  6. Example 1 • Are points E, F, and C collinear? • Are points E, F, and D collinear?

  7. Plane • flat surface that has no thickness • Think of a sheet of paper

  8. Coplanar • points and lines in the same plane

  9. Example 2 • Each surface of a cube represents part of a plane. Name the plane represented by the front of the cube.

  10. Postulates & Axioms • Accepted statements of facts • We will use these in proofs to formulate ideas

  11. Postulate 1-1 • Through any two points there is exactly one line.

  12. Postulate 1-2 • If two lines intersect, then they intersect in exactly one point.

  13. Postulate 1-3 • If two planes intersect, then they intersect in exactly one line.

  14. Example 3 • What is the intersection of plane HGFE and plane BCGF?

  15. Postulate 1-4 • Through any three noncollinear points there is exactly one plane.

  16. Example 4 • Shade the plane that contains A, B, and C.

  17. Example 4 • Shade the plane that contains E, H, and C.

  18. segment • part of a line consisting of two endpoints and all points between them

  19. ray • part of a line consisting of one endpoint and all the points of the line on one side of the endpoint

  20. opposite rays • two collinear rays with the same endpoint • always form a line!

  21. Example 5 • Name all of the segments and rays in the figure:

  22. parallel lines • coplanar lines that do not intersect

  23. skew lines • noncoplanar (not parallel and do not intersect)

  24. Example 6 • Name all segments parallel to DC. • Name all segments skew to DC.

  25. Parallel Planes • planes that do not intersect • a line and a plane that do not intersect are also parallel

  26. Example 7 • Use the diagram to name: • two pairs of parallel planes • a line that is parallel to plane GHIJ

  27. Homework… • p. 19: 2-8 even, 14, 20, 38, 40, 50, 52, 55-60 • p. 25: 12-23

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