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The Steiner-Lehmus theorem and "triangles with congruent medians are isosceles" hold in weak geometries

Authors
  • Pambuccian, Victor
  • Struve, Horst
  • Struve, Rolf
Type
Preprint
Publication Date
Jan 08, 2015
Submission Date
Jan 08, 2015
Identifiers
arXiv ID: 1501.01857
Source
arXiv
License
Yellow
External links

Abstract

We prove that (i) a generalization of the Steiner-Lehmus theorem due to A. Henderson holds in Bachmann's standard ordered metric planes, (ii) that a variant of Steiner-Lehmus holds in all metric planes, and (iii) that the fact that a triangle with two congruent medians is isosceles holds in Hjelmslev planes without double incidences of characteristic $\neq 3$.

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