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Euclid's Axiom

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• Euclid's Axiom
  
  
  Given a straight line and a point not on it, there is exactly one straight line passing through the given point and parallel to the given line.
  
  
• When the Euclid's Axiom is hypothesized, the following holds:
  
  
  • If a straight line intersects two straight lines, then each of the followings is necessary and sufficient for the two lines to be parallel:
    1. two alternate angles are equal in measure
    2. two corresponding angles are equal in measure
    3. two interior angles on the same side of a transversal are supplementary
  
  
• Implications of Euclid's Axiom
  
  
  • The sum of the magnitudes of the inner angles of a triangle is 2R.

Parallelims of straight lines Euclid's Axiom Given a straight line and a point not on it, there is exactly one straight line passing through the given point and parallel to the given line. Parallelims of line segments, rays // Drawing a straight line parallel to a given straight line passing through a point not on it