The Steiner-Lehmus theorem, stating that a triangle with two congruent interior bisectors must be isosceles, has received over the 170 years since it was first proved in 1840 a wide variety of proofs.

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 $$ e 3$$ .

He submitted to The American Mathematical Monthly, but apparently it was never published. Steiner-Lehmus Theorem Any Triangle that has two equal Angle Bisectors (each measured from a Vertex to the opposite sides) is an Isosceles Triangle . This theorem is also called the Internal Bisectors Problem and Lehmus' Theorem . Steiner-Lehmus theorem.

1.4 The incircle and excircles. 1.5 The Steiner-Lehmus theorem. 1.6 The orthic triangle. 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 9 May 2012 (Steiner-Lehmus Theorem) Prove that a triangle with two equal angle bisectors is an isosceles triangle. · In triangle {\triangle ABC} , given that 14 Apr 2019 theorems in geometry: the Steiner's theorem for the trapezoid, Ptolemy's and the Steiner-Lehmus theorem, The Mathematics Teacher 85(5).

Steiner–Lehmus theorem: lt;p|>The |Steiner–Lehmus theorem|, a theorem in elementary geometry, was formulated by |C. L. Le World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled.

DOI: 10.2307/2312796 Corpus ID: 124646269. The Steiner-Lehmus Theorem @article{Gilbert1963TheST, title={The Steiner-Lehmus Theorem}, author={G. Gilbert and D

This is an issue which has attracted along the 2014-10-28 · In the paper different kinds of proof of a given statement are discussed.

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. We also present some comments on possible intuitionistic approaches. (en) Mowaffaq Hajja, « A short trigonometric proof of the Steiner-Lehmus theorem », Forum Geometricorum, vol.
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The Steiner–Lehmus theorem, a theorem in elementary geometry, was formulated by C. L. Lehmus and subsequently proved by Jakob Steiner. It states: Every triangle with two angle bisectors of equal lengths is isosceles.

Unlike The seventh criterion for an isosceles triangle. The Steiner-Lehmus theorem. If in a triangle two angle bisectors are equal in measure, then this triangle is an isosceles triangle. The Steiner-Lehmus theorem.
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"Teorema de Gergonne-Steiner-Lehmus”, no qual consideramos a igualdade de duas cevianas de Mowaffaq, Other Versions of Steiner-Lehmus Theorem.

Prove dirette . Il teorema di Steiner-Lehmus può essere dimostrato usando la geometria elementare dimostrando l'affermazione contropositiva.

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If two bisectors are the same length in a triangle, it is isosceles.. The sentence was mentioned for the first time in 1840 in a letter from CL Lehmus to Charles-François Sturm, in which this Sturm asked for elementary geometric DOI: 10.1111/J.1949-8594.1939.TB03972.X Corpus ID: 122796278. THE LEHMUS-STEINER THEOREM @article{MacKay1939THELT, title={THE LEHMUS-STEINER THEOREM}, author={David L 2014-10-01 In 1844 [6], Steiner gave the ﬁrst proof of the following theorem.