triangle. n. 1. (Mathematics) geometry a three-sided polygon that can be classified by angle, as in an acute triangle, or by side, as in an equilateral triangle. Sum of interior angles: 180°; area: base × height. 2. any object shaped like a triangle. 3. any situation involving three parties or points of view. See also eternal triangle. 4. (Instruments) music a percussion instrument consisting of a sonorous metal bar bent into a triangular shape, beaten with a metal stick.