Introduction to Geometry

• Point


  • Image: dot [ ᐧ ]
  • How to name: ᐧP (read as point P)
  • It has no length, width or thickness and occupies no space
• Line


  • Image:
  • How to name: line l or
  • Has infinite length but has no width and thickness and it is straight
• Naming lines with multiple points


  • Line m
  • WX
  • XY
  • WY
• Plane


  • Image:
  • How to name: Plane P or Plane ABC
  • Has infinite length and width, but no thickness and it is a flat surface
• Other terms


  • SPACE - set of all points
  • FIGURE - any set of points
  • COPLANAR - set of points that lie on the same plane
  • COLLINEAR - points that lie on the same line
  • NON-COLLINEAR - points that do not lie on the same line
  • NON-COPLANAR - points that do not lie on the same plane
  • A, B and D are collinear
  • A, B and C are non-collinear
  • A, B, C and D are coplanar
  • Points that do not lie on the plane are non-coplanar
• Intersecting lines


  Two lines that meet at a common point
• Perpendicular lines


  • Two lines are perpendicular if they intersect and form right angles
  • Symbol for perpendicular: ⟂

  
• Parallel lines


  • Coplanar lines that do not meet
  • Symbol for parallel: //
• Concurrent lines


  Three or more lines that have a common point
• Parallel planes


  Planes that have no common points
• Skew lines


  Two lines that are not coplanar
• Intersecting planes


  Planes that intersect on a line
• Segment


  • It is a part of a line
  • A segment has two endpoints
• Ray


  • It is another part of a line
  • It has one endpoint and a part that is continuously extending
• Angle


  • It is formed by two non-collinear rays that have a common endpoint
  • The endpoint is the vertex of the angle
  • Each ray is the side of the angle
• Naming angles


  • ∠B
  • ∠ABC
  • ∠𝜃
• Acute angle


  An angle whose measure is greater than 0 but less than 90
• Right angle


  An angle whose measure is exactly 90
• Obtuse angle


  An angle whose measure is greater than 90 but less than 180