The Steiner-Lehmus Theorem states that a triangle with two internal angle bisectors of equal length, each measured from a vertex to the opposite side, must be isosceles. Named for Jakob Steiner and Daniel Christian Ludolph Lehmus, it is a classical result of elementary triangle geometry notable for being considerably harder to prove directly than its converse, that an isosceles triangle has two equal angle bisectors, which follows immediately from symmetry.
Facts
StatementEvery triangle with two angle bisectors of equal lengths is isosceles. 1 Proof Method Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Steiner-Lehmus theorem, Wikipedia
Principal Result Of
Source Steiner-Lehmus theorem, Wikipedia
Proved By
Source Steiner-Lehmus theorem, Wikipedia
Sources
1. Steiner-Lehmus theorem, Wikipedia
Lead, first sentence
Every triangle with two angle bisectors of equal lengths is isosceles.
Principal Result Of: Jakob Steiner, Lead sentence of the article on the result
Lehmus and subsequently proved by Jakob Steiner.
- In Branch: Geometry, Lead sentence
Proved By: Jakob Steiner, Lead sentence, attribution
subsequently proved by Jakob Steiner
View the Source2. ProofWiki: Steiner-Lehmus Theorem
ProofWikiProof sectionQuote, Proof section
Aiming for a contradiction, suppose $b \ne a$.
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