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The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
Problems of this type are included in the Moscow Mathematical Papyrus and Rhind Mathematical Papyrus. [51] The theorem that the base angles of an isosceles triangle are equal appears as Proposition I.5 in Euclid. [52] This result has been called the pons asinorum (the bridge of asses) or the isosceles triangle theorem. Rival explanations for ...
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 ...
Download as PDF; Printable version; In other projects ... Angle bisector theorem; ... Stewart's theorem; Sylvester's triangle problem; T. Thomsen's theorem This page ...
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
This subdivision of a triangle is a special case of a theorem of Richard Courant and Herbert Robbins that any plane area can be subdivided into four equal parts by two perpendicular lines, a result that is related to the ham sandwich theorem. [4] Although the triangle quadrisection has a solution involving the roots of low-degree polynomials ...