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

TL;DR

This paper provides a trigonometric proof of the Steiner-Lehmus Theorem within hyperbolic geometry, demonstrating that equal internal bisectors imply an isosceles triangle.

Contribution

It introduces a novel trigonometric proof of the Steiner-Lehmus Theorem specifically for hyperbolic geometry, extending classical Euclidean results.

Findings

Equal internal bisectors imply the triangle is isosceles in hyperbolic geometry

The proof uses hyperbolic trigonometric identities

The theorem holds in the hyperbolic plane

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.