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Neutral Geometry (NEUT)

In: Euclidean Geometry and its Subgeometries

Author

Listed:
  • Edward John Specht

    (Indiana University South Bend)

  • Harold Trainer Jones

    (Andrews University)

  • Keith G. Calkins

    (Ferris State University)

  • Donald H. Rhoads

    (Andrews University)

Abstract

This chapter deals with neutral geometry, which is central to the entire book. It begins with definitions of mirror mappings and reflections over lines. Every line is an axis for some reflection. A line of symmetry for a set is a line whose reflection maps that set onto itself. Every angle has a line of symmetry, its angle bisector. Compositions of reflections are isometries, and isometric sets are congruent. These concepts provide access to the standard congruence theorems. Reflections are used to define perpendicularity, the perpendicular bisector and midpoint of a segment, and to prove the existence of a line (not necessarily unique) through a given point parallel to a given line. Ordering of angles is defined, leading to the notions of acute angle, obtuse angle, and maximal angle of a triangle.

Suggested Citation

  • Edward John Specht & Harold Trainer Jones & Keith G. Calkins & Donald H. Rhoads, 2015. "Neutral Geometry (NEUT)," Springer Books, in: Euclidean Geometry and its Subgeometries, edition 1, chapter 0, pages 155-224, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-23775-6_8
    DOI: 10.1007/978-3-319-23775-6_8
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