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
Classification
Statement FormCharacterization Theorem 1 StatementEvery triangle with two angle bisectors of equal lengths is isosceles. 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
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.
- In Branch: Geometry, Lead sentence
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