The Steiner–Lehmus theorem and “triangles with congruent medians are isosceles” hold in weak geometries

Victor Pambuccian, Horst Struve, Rolf Struve

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We prove that (a) a generalization of the Steiner–Lehmus theorem due to A. Henderson holds in Bachmann’s standard ordered metric planes, (b) that a variant of Steiner–Lehmus holds in all metric planes, and (c) that the fact that a triangle with two congruent medians is isosceles holds in Hjelmslev planes without double incidences of characteristic ≠ 3.

Original languageEnglish (US)
Pages (from-to)483-497
Number of pages15
JournalBeitrage zur Algebra und Geometrie
Volume57
Issue number2
DOIs
StatePublished - Jun 1 2016

Keywords

  • Bachmann’s ordered metric planes
  • Equal medians
  • Hjelmslev groups
  • Steiner–Lehmus theorem

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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