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- Hinge_theorem abstract "In geometry, the hinge 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. This theorem is actually Propositions 24 of Book 1 of Euclid's Elements (sometimes is called the open mouth theorem). The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.It can be also extended from the plane euclidean geometry to higher dimensions euclidean spaces (i.e., for tetrahedra and more general for simplices), as it was done recently by S. Abu-Saymeh, M. Hajja, M. Hayajneh in for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent)and more generally by M. Hajja and M. Hayajneh in for orthocentric simplices (i.e., simplices in which altitudes are concurrent).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. In some textbooks, the theorem and its converse are written as the SAS Inequality Theorem and the SSS Inequality Theorem respectively.".
- Hinge_theorem wikiPageID "3570709".
- Hinge_theorem wikiPageRevisionID "604964569".
- Hinge_theorem date "April 2014".
- Hinge_theorem hasPhotoCollection Hinge_theorem.
- Hinge_theorem reason "This article needs to be divided into sections, and references need to be added".
- Hinge_theorem subject Category:Elementary_geometry.
- Hinge_theorem subject Category:Theorems_in_geometry.
- Hinge_theorem subject Category:Triangle_geometry.
- Hinge_theorem type Abstraction100002137.
- Hinge_theorem type Communication100033020.
- Hinge_theorem type Message106598915.
- Hinge_theorem type Proposition106750804.
- Hinge_theorem type Statement106722453.
- Hinge_theorem type Theorem106752293.
- Hinge_theorem type TheoremsInGeometry.
- Hinge_theorem comment "In geometry, the hinge 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. This theorem is actually Propositions 24 of Book 1 of Euclid's Elements (sometimes is called the open mouth theorem).".
- Hinge_theorem label "Hinge theorem".
- Hinge_theorem label "Scharnierstelling".
- Hinge_theorem sameAs Scharnierstelling.
- Hinge_theorem sameAs m.09m8bg.
- Hinge_theorem sameAs Q2607007.
- Hinge_theorem sameAs Q2607007.
- Hinge_theorem sameAs Hinge_theorem.
- Hinge_theorem wasDerivedFrom Hinge_theorem?oldid=604964569.
- Hinge_theorem isPrimaryTopicOf Hinge_theorem.