Quadrilateral

In geometry, a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side". It is also called a tetragon, derived from Greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices A {\displaystyle A} , B {\displaystyle B} , C {\displaystyle C} and D {\displaystyle D} is sometimes denoted as ◻ A B C D {\displaystyle \square ABCD} . Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees, that is ∠ A + ∠ B + ∠ C + ∠ D = 360 ∘ . {\displaystyle \angle A+\angle B+\angle C+\angle D=360^{\circ }.} This is a special case of the n-gon interior angle sum formula: S = (n − 2) × 180° (here, n=4). All non-self-crossing quadrilaterals tile the plane, by repeated rotation around the midpoints of their edges.