A Wild Steiner-Lehmus Chase

TL;DR

This paper provides a new proof of the Steiner-Lehmus equal bisectors theorem using the Law of sines, addressing a long-standing mathematical challenge with a novel approach.

Contribution

It introduces a rapid succession application of the Law of sines to prove the Steiner-Lehmus theorem, offering a fresh perspective on a classical geometric problem.

Findings

Successful proof of the Steiner-Lehmus theorem using Law of sines

New methodological approach to classical geometry problems

Addresses historical interest in direct proofs

Abstract

We present a proof the Steiner-Lehmus equal bisectors theorem by applying the Law of sines in rapid succession to a side-by-side comparison. For nearly two centuries, the quest for a direct proof has sustained interest in proving and reproving this theorem. We suggest that a second driving force may also be at play.