triangle

The exterior angle of a triangle is equal to the sum of the opposite interior angles.

In geometry, a three-sided plane figure, the sum of whose interior angles is 180°. Triangles can be classified by the relative lengths of their sides. A scalene triangle has three sides of unequal length. An isosceles triangle has at least two equal sides; it has one line of symmetry. An equilateral triangle has three equal sides (and three equal angles of 60°); it has three lines of symmetry.

Triangles can also be classified by their angle measures: a right triangle has one right (90°) angle; an acute triangle has three acute (less than 90°) angles; an obtuse triangle has one obtuse (greater than 90°) angle; an equiangular triangle has three equal angles. (All equilateral triangles are equiangular, and vice versa.) If the length of one side of a triangle is l and the perpendicular distance from that side to the opposite corner is h (the height or altitude of the triangle), its area A = 1/2 (lh).

triangle

Small percussion instrument consisting of a thin metal bar bent into the shape of a triangle. Hit by a metal rod, it produces a tinkling tone of high, indefinite pitch. Compositions that call for a prominent triangle part include Liszt's Piano Concerto in E flat (1849; revised 1853, 1856) and the third movement of Brahms' Fourth Symphony (1885).