quadrilatero

Quadrilatero is the Italian word for quadrilateral, a polygon with four sides and four vertices. In geometry, quadrilaterals include many familiar shapes such as rectangles, squares, parallelograms, trapezoids, and more generally any four-sided figure.

Quadrilaterals are classified by their interior angles and by their parallel sides. Simple quadrilaterals are either convex, with all interior angles less than 180 degrees, or concave, with one interior angle greater than 180 degrees. A crossed or complex quadrilateral is self-intersecting, producing a bow-tie shape.

Common subclasses by sides and angles include parallelograms (opposite sides are parallel), rectangles (parallelograms with right angles), rhombuses (parallelograms with equal sides), and squares (rectangles that are also rhombuses). Trapezoids (one pair of parallel sides) and isosceles trapezoids are also standard classifications; in a cyclic quadrilateral, opposite angles sum to 180 degrees.

A key geometric property is that the sum of interior angles in any simple quadrilateral is 360 degrees. A diagonal divides a quadrilateral into two triangles, a fact used in many area and congruence calculations. In parallelograms, the diagonals bisect each other, and in rectangles the diagonals are equal in length.

In Italian usage, quadrilatero can also denote a geographic area. The Quadrilatero della Moda, or fashion quadrilateral, is a well-known district in Milan bounded by Via Montenapoleone, Via della Spiga, Via Sant’Andrea, and Via Borgospeso, celebrated for luxury fashion houses and high-end shopping.