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 \(\ne 3\).
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Pambuccian, V., Struve, H. & Struve, R. The Steiner–Lehmus theorem and “triangles with congruent medians are isosceles” hold in weak geometries. Beitr Algebra Geom 57, 483–497 (2016). https://doi.org/10.1007/s13366-015-0278-y
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DOI: https://doi.org/10.1007/s13366-015-0278-y