The Steiner-Lehmus Theorem is famous for its indirect proof. I wanted to come up with a 'direct' proof for it (of course, it can't be direct because some theorems used, will, of course, be indirect

In December 2010, Charles Silver of Berkeley, CA, devised a direct proof of the Steiner-Lehmus theorem, which uses only compass and straightedge and relies entirely on notions from Book I of Euclid's Elements. He submitted to The American Mathematical Monthly, but apparently it was never published.

The theorem was first mentioned in 1840 in a letter by C. L. Lehmus to C. Sturm, in which he asked for a purely geometric proof.C. Sturm passed the request on to other The theorem of Steiner–Lehmus states that if a triangle has two (internal) angle-bisectors with the same length, then the triangle must be isosceles (the converse is, obviously, also true). This is an issue which has attracted along the 2015-12-26 2009-09-08 Steiner-Lehmus theorem states that if the internal angle bi-sectors of two angles of a triangle are equal, then the trian-gle is isosceles [1]. Lemma 1 (Sines Theorem) In the hyperbolic trian-gle ABC let α,β,γdenote at A,B,C and a,b,c denote the hyperbolic lengths of the sides opposite A,B,C, The Steiner-Lehmus theorem is a theorem of elementary geometry about triangles.. It was first formulated by Christian Ludolf Lehmus and then proven by Jakob Steiner..

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. One theorem that excited interest is the internal bisector problem.

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.

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 .

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

Proof of the theorem. The Steiner-Lehmus Theorem is famous for its indirect proof. I wanted to come up with a 'direct' proof for it (of course, it can't be direct because some theorems used, will, of course, be indirect 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. The theorem of Steiner–Lehmus states that if a triangle has two (internal) angle-bisectors with the same length, then the triangle must be isosceles (the converse is, obviously, also true). 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. Detailed descriptions of direct and indirect methods of proof are given.

Introduction. In 1840 C. L. Lehmus sent the following problem to Charles Sturm: "Direct Proof" of the Steiner-Lehmus Theorem Since an angle bisector divides the third side into the same ratio as the ratio of the other two sides, I set m=kc, n=k b KEIJI KIYOTA. Abstract. We give a trigonometric proof of the Steiner-Lehmus Theorem in hyperbolic geometry.
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Proof of the theorem. 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 .

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. steiner lehmus theorem In December 2010, Charles Silver of Berkeley, CA, devised a direct proof of the Steiner-Lehmus theorem, which uses only compass and straightedge and relies entirely on notions from Book I of Euclid's Elements.
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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. The theorem was first mentioned in 1840 in a letter by C. L. Lehmus to C. Sturm, in which he asked for a purely geometric proof.

The Steiner-Lehmus Theorem has garnered attention since its conception and The well known Steiner-Lehmus theorem states that if the internal angle bisec- tors of two angles of a triangle are equal, then the triangle 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.

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In 1844 [6], Steiner gave the ﬁrst proof of the following theorem. If two internal bisectors of a triangle on the Euclidean plane are equal, then the triangle is isosceles. This had been originally asked by Lehmus in 1840, and now is called the Steiner-Lehmus Theorem. Since then, wide variety of proofs have been given by many people over 170

It states: Every triangle with two angle bisectors of equal lengths is isosceles. The theorem was first mentioned in 1840 in a letter by C. L. Lehmus to C. Sturm, in which he asked for a purely geometric proof. Steiner·Lehmus Theorem Let ABC be a triangle with points 0 and E on AC and AB respectively such that 80 bisects LABC and CE bisects LACB.