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1.6 – Planes and the Space of Geometry

Objectives

  • Define the three dimensions of length, width, and height.
  • Define and identify collinear points and coplanar points and lines.
  • Identify objects that are zero-, one-, two-, and three-dimensional.
  • Relate the concept of infinity to one-, two-, and three-dimensional objects.

 

Key Terms

  • Infinite – having no boundary or limit.
  • Collinear – lying in a straight line. Three or more points are collinear if a straight line can be drawn through all of them.
  • Plane – a flat surface that extends forever in all directions (infinite). A plane has no thickness, so it has only two dimensions (length and width).
  • Coplanar – lying in the same plane. Four or more points are coplanar if there is a plane that contains all of them.
  • Zero-Dimensional – having no length, width, or height (ex. points)
  • One-Dimensional – having length but no width or height (ex. lines, line segments, rays)
    • one-dimensional with infinite length: lines and rays
    • one-dimensional with measurable length: line segments
  • Two-Dimensional – having length and width but no height (ex. planes / flat surfaces you can’t pick up)
  • Three-Dimensional – having length, width, and height (ex. solids, geometric space, our world, things you can grab and hold)

 

Notes

Dimensions
GeoA-01.06 Dimensions2

GeoA-01.06 Dimensions

GeoA-01.06 Dimensions3

Collinear
  • If you have exactly two points, they will ALWAYS be collinear.
  • If you have more than two points, they might be collinear, but they might not.
  • Three or more points are collinear if a line can be drawn through ALL of them

GeoA - 1.06 Collinear 2

GeoA - 1.06 Collinear

Coplanar
  • If three points are collinear, they are also coplanar
  • Two lines are guaranteed to be coplanar if they lie in the same plane.
  • Two lines and a point are guaranteed to be coplanar if they lie in the same plane.
  • Four points are always coplanar if they lie on the same line (collinear) AND lie in the same plane.

GeoA - 1.06 Coplanar

 

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