Step angle set

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Step angle theorem: α = β

The step angle theorem is a mathematical theorem . It says: If two parallel straight lines a and b are intersected by a third straight line c, the step angles are the same.

The step angle theorem is reversible, ie the following applies: If two straight lines a and b are intersected by a third straight line c and the step angles are equal, then a and b are parallel.

literature

  • Hans Schupp: Elementary Geometry . Schöningh, Hannover 1977, ISBN 3-506-99189-2 . , P. 37
  • Hendrik Kasten, Denis Vogel: Fundamentals of plane geometry . Springer 2018, pp. 78–81

Web links

  • Yann-Martin Jeannès: The problem of parallels . Proseminar preparation, Technical University Dortmund, winter semester 2016/17