Rhombus - Characterizations

Characterizations

A simple (non self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following:

• a quadrilateral with four sides of equal length (by definition)
• a quadrilateral in which the diagonals are perpendicular and bisect each other
• a quadrilateral in which each diagonal bisects two opposite interior angles
• a parallelogram in which at least two consecutive sides are equal in length
• a parallelogram in which the diagonals are perpendicular
• a parallelogram in which a diagonal bisects an interior angle