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Pages in category "Theorems about triangles" The following 29 pages are in this category, out of 29 total. This list may not reflect recent changes. A.
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures; List of data structures; List of derivatives and integrals in alternative calculi; List of equations; List of fundamental theorems; List of hypotheses; List of inequalities; Lists of ...
Pages in category "Theorems in geometry" The following 48 pages are in this category, out of 48 total. ... Triangle inequality; U. Ultraparallel theorem; W.
Pages in category "Theorems about triangles and circles" The following 18 pages are in this category, out of 18 total. This list may not reflect recent changes. C.
Triangle inequality: If a, b, and c are the lengths of the sides of a triangle 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 vectors and vector lengths :
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
[59] [60] Thus, right triangles in a non-Euclidean geometry [61] do not satisfy the Pythagorean theorem. For example, in spherical geometry, all three sides of the right triangle (say a, b, and c) bounding an octant of the unit sphere have length equal to π /2, and all its angles are right angles, which violates the Pythagorean theorem because
For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number , except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°).
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