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The converse of the hinge theorem is also true: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.
The hinge theorem or 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.
Euler's theorem in geometry; Gromov's inequality for complex projective space; Gromov's systolic inequality for essential manifolds; Hadamard's inequality; Hadwiger–Finsler inequality; Hinge theorem; Hitchin–Thorpe inequality; Isoperimetric inequality; Jordan's inequality; Jung's theorem; Loewner's torus inequality; Łojasiewicz inequality ...
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.
In the mathematical theory of automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to be the Mellin transform of a modular form. More generally a converse theorem states that a representation of an algebraic group over the adeles is automorphic whenever the L-functions of various twists of it are well-behaved.
Rigorously, a subderivative of a convex function : at a point in the open interval is a real number such that () for all .By the converse of the mean value theorem, the set of subderivatives at for a convex function is a nonempty closed interval [,], where and are the one-sided limits = (), = + ().
Hinge has found that daters prefer voice prompts as a way to get to know a person better before meeting up in real life. To add a voice prompt, go to your profile and find it underneath the photo ...
Theorem. [2] [3] If a framework is infinitesimally rigid, then it is rigid. The converse of this theorem is not true in general; however, it is true for generic rigid frameworks (with respect to infinitesimal rigidity), see combinatorial characterizations of generically rigid graphs.