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

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Preprint
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arXiv ID: 1501.01857
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arXiv
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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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