A trigonometric proof of the Steiner-Lehmus Theorem in hyperbolic geometry

2015/08/13 by Keiji Kiyota, Kiyota, Keiji
Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1508.03248

openalex publication_date 2015/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a trigonometric proof of the Steiner-Lehmus Theorem in hyperbolic geometry. Precisely we show that if two internal bisectors of a triangle on the hyperbolic plane are equal, then the triangle is isosceles.

Related

• The Steiner-Lehmus theorem and "triangles with congruent medians are isosceles" hold in weak geometries
• 109.48 A generalisation and proof of the Steiner–Lehmus Theorem
• Hyperbolic plane geometry revisited
• A Machine-Checked Direct Proof of the Steiner-Lehmus Theorem
• Duality between Hyperbolic and de Sitter Geometry