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Triangle inequality - Wikipedia

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In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.[1][2] This statement permits the inclusion of degenerate triangles, but some authors, especially those writing about elementary geometry, will exclude this possibility, thus leaving out the possibility of equality.[3] If x, y, and z are the lengths of the sides of the triangle, with no side being greater than z, then the triangle inequality states that with equality only in the degenerate case of a triangle with zero area. In Euclidean geometry and some other geometries, the triangle inequality is a theorem about distances, and it is written using vectors and vector lengths (norms): where the length z of the third side has been replaced by the vector sum x + y. When x and y are real numbers, they can be viewed as vectors in 𝑅 1 , and the triangle inequality expresses a relationship between absolute values. In

Triangle inequality - Wikipedia Jump to content From Wikipedia, the free encyclopedia Property of geometry, also used to generalize the notion of "distance" in metric spaces c\\le a+b</math><!-- DO NOT USE {{math}}. IT DOES NOT WORK INSIDE HATNOTES. -->"},"2":{"wt":"other inequalities associated with triangles"},"3":{"wt":"List of triangle inequalities"}},"i":0}}]}'> This article is about the basic inequality c ≤ a + b {\displaystyle c\leq a+b} . For other inequalities associated with triangles, see List of triangle inequalities . Three examples of the triangle inequality for triangles with si

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