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Points, Lines, and Planes

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talia
40 diapositives · 578 Views · Jul 30, 2014

This guide explores the fundamental concepts of geometry, detailing the nature of points, lines, and planes. A point is defined as an exact location in space with no dimensions. Lines are one-dimensional, extending infinitely in both directions and are formed by two distinct points. Rays have a starting point and extend infinitely, while line segments have both a starting and ending point. Additionally, we delve into the relationships between lines, including intersecting, parallel, and skew lines, as well as the properties of planes, which are two-dimensional and can also be intersecting or parallel.

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Points, Lines, and Planes
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  1. Points, Lines, and Planes

  2. A point is an exact location in space. You are here.

  3. A true point has no length, no width, and no height. In fact, you cannot see a true point.

  4. A point is named by a letter. Point P P

  5. Lines are 1-dimensional objects that have only length. Lines continue forever in both directions.

  6. Because a line has no width or height, you cannot see a true line.

  7. A line is defined by 2 points. A B Line AB

  8. A ray has a starting point but no ending point.

  9. A ray of light has a starting point (like the sun) and continues forever in the same direction.

  10. Of course, if the ray hits an object, the light could be absorbed or reflected. MIRROR

  11. A ray is also defined by 2 points. C D Ray CD

  12. A line segment has a starting point and an ending point. Line segments can be measured.

  13. A line segment also defined by 2 points. E F Line Segment EF

  14. Lines can do various things.

  15. Lines can intersect at a point to form angles. X Y Z

  16. When lines intersect to form right angles, they are said to be perpendicular. R UT RV c S T U V

  17. Lines do not always intersect.

  18. Lines can be parallel.

  19. Parallel lines have the same slope or steepness.

  20. Is it possible for lines not to intersect and not be parallel either?

  21. Believe it or not, this is possible.Let’s consider a 3-dimensional rectangular prism.

  22. These 2 lines are not parallel, but they are not intersecting either.

  23. These lines are called skew lines.

  24. You might have heard the word “skewer” the last time you had a barbecue. S K E W E R

  25. A skewer raises your “dinner” off the surface of the grill. The skewer does not intersect the grill, and the skewer is not parallel to the grill.

  26. Lines can be… intersecting skew parallel perpendicular 90º

  27. A plane is a flat surface that has length & width but no height.

  28. You can see a plane only if you view it at a certain angle.

  29. A true plane goes on forever in all directions.

  30. A true plane goes on forever in all directions.

  31. A true plane goes on forever in all directions.

  32. A true plane goes on forever in all directions.

  33. A true plane goes on forever in all directions.

  34. Planes can…

  35. Planes can intersect.

  36. An X-Wing fighter from Star Wars has wings that intersect.

  37. Planes can be perpendicular.

  38. Planes can be parallel.

  39. A Tie Fighter from Star Wars has wings that are parallel.

  40. Planes can be… intersecting parallel perpendicular