Neutral Geometry (NEUT)

Edward John Specht, Harold Trainer Jones, Keith G. Calkins and Donald H. Rhoads
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Edward John Specht: Indiana University South Bend
Harold Trainer Jones: Andrews University
Keith G. Calkins: Ferris State University
Donald H. Rhoads: Andrews University

Chapter Chapter 8 in Euclidean Geometry and its Subgeometries, 2015, pp 155-224 from Springer

Abstract: 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.

Keywords: Neutral Geometry (NEUT); Congruence Theorem; Isometric Sets; Perpendicular Bisector; Reflection Sets (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/978-3-319-23775-6_8

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