Quadrilateral

A polygon with four sides and four vertices. Its interior angles sum to 360 degrees, and its sides can form many distinct classes of shape.

Polygon: A closed plane figure formed by a finite sequence of straight line segments. A quadrilateral is the four-sided member of this broader family.
Angle sum of a polygon: A rule relating a polygon’s number of sides to the sum of its interior angles. Splitting a quadrilateral into two triangles proves its interior angle sum is 360 degrees.
Kite (geometry): A quadrilateral with two distinct pairs of adjacent sides equal in length. Its adjacent equal-side condition defines a family not based on parallel sides.
Rectangle: A quadrilateral with four right angles. Every rectangle is a parallelogram, but not every rectangle has four equal sides.
Area: A measure of the amount of two-dimensional space enclosed by a shape. Quadrilateral area formulas measure land, surfaces, and plane figures.
Vertex (geometry): A point where two or more geometric lines, rays, or segments meet. Four vertices mark the corners where a quadrilateral’s sides join.
Triangle: A polygon with three sides and three interior angles. A diagonal divides a quadrilateral into two triangles for many geometric proofs.
Cyclic quadrilateral: A quadrilateral whose four vertices lie on one circle. Opposite angles in this special case are supplementary.
Rhombus: A quadrilateral with four sides of equal length. A rhombus need not have right angles, despite sharing equal sides with a square.
Brahmagupta's formula: A formula for the area of a cyclic quadrilateral using its four side lengths and semiperimeter. It gives the area from side lengths when the quadrilateral is cyclic.

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