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

2015/01/08 by Pambuccian, Victor, Struve, Horst, Struve, Rolf
#51F05 #51F15 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1501.01857

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 ≠ 3.

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