1 / 15

Understanding 3D Geometry: Points, Lines, and Planes

Learn the basics of points, lines, and planes in geometry, including collinear and noncollinear points, intersections, and coplanar concepts.

dorothysanchez
Download Presentation

Understanding 3D Geometry: Points, Lines, and Planes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 1.2 Points, Lines, And Planes Geometry

  2. Point: • A Location in Space • Has No Size • Name a point with a CAPITAL LETTER and represent it with a dot • Line: • Straight Path of Points • No Thickness • Extends Infinitely in Opposite Directions t A B

  3. A C • Collinear: • Three or more points on a line. • Noncollinear: • Points do not form a line. B ● ● B ● ● ● ● A C

  4. Ex.1) Identify Collinear Points • Are the following points collinear? • A, E, C • G, F, B • D, E, A • Name line m in three other ways • Name line l in three other ways

  5. PLANE R . S . T . X • Flat Surface/No Thickness • Infinite Number of Points and Lines • Extends Without End • Any 3 Noncollinear Points ALWAYS Make a Plane • Name a Plane • A Capital Letter or • At Least 3 of its Noncollinear Points Plane RST or Plane X

  6. Ex.2) Name the Plane The Bottom The Top The Front The Back The Left Side The Right Side A B D C E F H G

  7. COPLANAR R .S . T. X Lines or points in the same plane.

  8. t A B P ● m n Line t is the only line that passes through points A and B. Postulate 1-1 Two lines intersect in exactly one point. Lines m and n intersect at point P. Postulate 1- 2 Through any 2 points there is exactly one line.

  9. A line and a plane intersect, in exactly one point.

  10. Postulate 1-3 ●A ●B ●C D t Plane ABC and Plane D intersect at line t. Two planes intersect, in exactly one line.

  11. M P L Picture this cube as having Planes M, L and P. They intersect in 3 separate lines.

  12. Ex.3) Name the intersection of Planes ABC & BFG Name two planes that intersect the given line. A B D C E F H G

  13. Can you name sets of noncollinear points? A B D C E F Postulate 1-4 Through any 3 noncollinear points there is exactly one plane. H G

  14. A B D C E F Find Planes: ABC HEF BCG ADG H G

  15. Ex.4) • Shade the plane containing points A, E, F • Name another point in Plane EHG • Is point F coplanar with plane DCG? A B D C E F H G

More Related