# The seventh criterion for an isosceles triangle. The Steiner-Lehmus theorem. If in a triangle two angle bisectors are equal. Proof of the theorem.

Hajja, Stronger forms of the Steiner-Lehmus theorem, Forum Geom. 8 (2008) 157 –161. 3. M. Hajja, On a morsel of Ross Honsberger, Math. Gaz. 93 (2009)

I started with Δ A B C, with angle bisectors B X and C Y, and set them as equal. The first obvious step was the … THE LEHMUS-STEINER THEOREM DAVID L. MACKAY, Evandcr Cliilds High School, New York City HISTORY In 1840 Professor Lehmus sent the following theorem to Jacob Steiner with a request for a purely geometric proof: If the bisectors of the angles at the base of a triangle, measured from the vertices to the opposite sides, are equal, the triangle is isosceles. steiner lehmus theorem About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features © 2020 Google LLC A geometry theorem Steiner-Lehmus theorem. Key Words: Steiner-Lehmus theorem MSC 2000: 51M04 1. Introduction The Steiner-Lehmus theorem states that if the internal angle-bisectors of two angles of a triangle are congruent, then the triangle is isosceles. Despite its apparent simplicity, the problem has proved more than challenging ever since 1840. The seventh criterion for an isosceles triangle.

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본문 기타 기능. 본문 폰트 크기 "Teorema de Gergonne-Steiner-Lehmus”, no qual consideramos a igualdade de duas cevianas de Mowaffaq, Other Versions of Steiner-Lehmus Theorem. Steiner-Lehmus Theorem: Surhone, Lambert M.: Amazon.se: Books. Den Steiner-Lehmus theorem , ett teorem i elementär geometri, formulerades av CL Lehmus och därefter bevisas av Jakob Steiner . Det står: Varje triangel med "Steiner Lehmus Theorem" · Book (Bog).

8, 2008, p. 39-42 ( lire en ligne ) . (en) Róbert Oláh-Gál et József Sándor, « On trigonometric proofs of the Steiner-Lehmus theorem » , Forum Geometricorum , vol.

## The indirect proof of Lehmus-Steiner’s theorem given in [2] has in fact logical struc ture as the described ab ove although this is not men tioned by the authors. Proof by construction.

2, p. 483.

### Steiner-Lehmus Theorem holds.[101 Yet Another Proof of the Steiner-Lehmus Theorem: It is necessary to point out that this proof does not have a reference In the bibliography of this paper as a proof of the Steiner-Lehmus Theorem. However, the proof does derIve a large part of Its development fram an

converse theorem correctly: Theorem 1 (Steiner-Lehmus). If two internal angle bisectors of a triangle are equal, then the triangle is isosceles. According to available history, in 1840 a Berlin professor named C. L. Lehmus (1780-1863) asked his contemporary Swiss geometer Jacob Steiner for a proof of Theorem 1.

Apply the Stewart's theorem for the cevians $BE$
Hajja, Stronger forms of the Steiner-Lehmus theorem, Forum Geom.

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Provides a proof that, if two angle bisectors of a triangle are equal in length, the triangle is isosceles (Steiner-Lehmus Theorem) using two corollaries related to a … 2014-10-28 By rephrasing quantifier-free axioms as rules of derivation in sequent calculus, we show that the generalized Steiner–Lehmus theorem admits a direct proof in classical logic. This provides a partial answer to a question raised by Sylvester in 1852.

It has its own name - The Steiner-Lehmus Theorem,- and its own story.

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### Steiner–Lehmus theorem The Steiner–Lehmus theorem, a theorem in elementary geometry, was formulated by C. L. Lehmus and subsequently proved by Jakob

Congruent Triangles. The Three Theorems. The Steiner–Lehmus theorem, a theorem in elementary geometry, was formulated by C. L. Lehmus and subsequently proved by Jakob Steiner.

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### We prove that (a) a generalization of the Steiner–Lehmus theorem due to A. Henderson holds in Bachmann’s standard ordered metric planes, (b) that a variant of Steiner–Lehmus holds in all metric planes, and (c) that the fact that a triangle with two congruent medians is isosceles holds in Hjelmslev planes without double incidences of characteristic $$ e 3$$ .

2, p. 483. Steiner-Lehmus Theorem. Hidekazu Takahashi. Header < < " E o s H e a d e r. m " I n THE LEHMUS‐STEINER THEOREM.

## In the paper different kinds of proof of a given statement are discussed. Detailed descriptions of direct and indirect methods of proof are given. Logical models illustrate the essence of specific types of indirect proofs. Direct proofs of Lehmus-Steiner's Theorem are proposed.

In Coxeter's book ”Geometry revisited” there Stewart's theorem · theorem of Stewart Satz von Solovay · Satz von Sperner · Satz von Steiner · Satz von Steiner-Lehmus; Satz von Stewart; Satz von Stokes (Proposed by Ali Abouzar/FB/Math) The statement is known as the ”Steiner-Lehmus theorem”.

Lehmus Theorem. The Steiner-Lehmus Theorem has long drawn the interest of edu-cators because of the seemingly endless ways to prove the theorem (80 plus accepted di erent proofs.) This has made the it a popular challenge problem. This character-istic of the theorem has also drawn the attention of many mathematicians who are The three Steiner-Lehmus theorems - Volume 103 Issue 557.