Dreieck

Dreieck is the German term for triangle, a polygon with three sides and three interior angles. In geometry, triangles are the simplest non-degenerate polygons and form the basis for many constructions and proofs. The sum of a triangle’s interior angles is always 180 degrees. Sides are commonly labeled a, b, and c, with opposite angles A, B, and C. Triangles are categorized by sides as equilateral (a = b = c), isosceles (two sides equal), or scalene (no equal sides), and by angles as acute (all angles less than 90°), right (one angle exactly 90°), or obtuse (one angle greater than 90°).

Key relations include the Pythagorean theorem for right triangles, a^2 + b^2 = c^2, and various area formulas: base times height over two, area = 1/2 ab sin C, or Heron’s formula using semiperimeter and side lengths. The triangle also has associated centers and circles, such as the circumcenter, incenter, centroid, and incircle, with standard constructions in Euclidean geometry.

Besides mathematics, the term is used for triangular shapes and formations in design, architecture, and navigation, reflecting its geometric meaning. Etymologically, the word derives from drei (three) and Eck (corner) in German. See also polygon, triangle, trigonometry.