A quadrilateral is a polygon that has exactly four sides, four vertices, and four angles. The word "quadrilateral" is derived from the Latin words "quadri," which means four, and "latus," which means side. There are many different types of quadrilaterals, including:

• Square: A square is a regular quadrilateral where all four sides are of equal length (equilateral), and all four angles are right angles. An equivalent condition is that opposite sides are parallel (a square is a parallelogram), and that the diagonals perpendicularly bisect each other and are of equal length.

• Rectangle: A rectangle is a parallelogram where all four angles are right angles. It has two pairs of opposite sides that are parallel and equal in length.

• Rhombus: A rhombus is a parallelogram where all four sides are of equal length (equilateral). Its opposite angles are equal, and its diagonals bisect each other at right angles.

• Trapezoid: A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases, and the non-parallel sides are called the legs.

• Kite: A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. Its diagonals intersect at right angles, and one diagonal bisects the other.

Quadrilaterals can also be classified as convex or concave. A convex quadrilateral has all its interior angles less than 180 degrees, while a concave quadrilateral has at least one interior angle greater than 180 degrees.