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In geometry, the hinge theorem (sometimes called the open mouth theorem) states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle. [1]
The parameters most commonly appearing in triangle inequalities are: the side lengths a, b, and c;; the semiperimeter s = (a + b + c) / 2 (half the perimeter p);; the angle measures A, B, and C of the angles of the vertices opposite the respective sides a, b, and c (with the vertices denoted with the same symbols as their angle measures);
Lieb–Thirring inequality; Littlewood's 4/3 inequality; Markov brothers' inequality; Mashreghi–Ransford inequality; Max–min inequality; Minkowski's inequality; Poincaré inequality; Popoviciu's inequality; Prékopa–Leindler inequality; Rayleigh–Faber–Krahn inequality; Remez inequality; Riesz rearrangement inequality; Schur test ...
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.
Take, for example, his royal tour of Australia and Samoa with wife Queen Camilla. The now-76-year-old monarch (yes, his birthday was yesterday and, yes, the family released a new portrait) made a ...
Chinese cars are selling at record levels in Russia. Competition from European, Korean, and Japanese carmakers has vanished since Western sanctions were imposed on Russia.
For example, Michelle Cosgrove's benefits were cut in half, reduced from $866 a month. Cosgrove spent the first half of her career as a paralegal, contributing to Social Security, before staying ...
For four points in order around a circle, Ptolemy's inequality becomes an equality, known as Ptolemy's theorem: ¯ ¯ + ¯ ¯ = ¯ ¯. In the inversion-based proof of Ptolemy's inequality, transforming four co-circular points by an inversion centered at one of them causes the other three to become collinear, so the triangle equality for these three points (from which Ptolemy's inequality may ...