Triangle Category

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted A B C {\displaystyle \triangle ABC}. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i. e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it, however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted. Types of triangle The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of Euclid's Elements. The names used for modern classification are either a direct transliteration of Euclid's Greek or their Latin translations. = By lengths of sides =Ancient Greek mathematician Euclid defined three types of triangle according to the lengths of their sides:Greek: , , , lit. 'Of trilateral figures, an isopleuron [equilateral] triangle is that which has its three sides equal, an isosceles that which has two of its sides alone equal, and a scalene that which has its three sides unequal. 'An equilateral triangle (Greek: , romanized: ispleuron, lit. 'equal sides') has three sides of the same length.

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