A rhombus is a quadrilateral plane figure, closed shape, four sides with four equal-length sides and opposite sides parallel to each other. All rhombuses are parallelograms, but not all parallelograms are rhombuses. All squares are rhombuses, but not all rhombuses are squares. The opposite interior angles of rhombuses are congruent. Diagonals of a rhombus always bisect each other at right angles. You can build a rhombus right now, on any flat surface, if you have four identical, linear objects.
In plane Euclidean geometry , a rhombus plural rhombi or rhombuses is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral , since equilateral means that all of its sides are equal in length. Every rhombus is simple non-self-intersecting , and is a special case of a parallelogram and a kite. A rhombus with right angles is a square. The surface we refer to as rhombus today is a cross section of the bicone on a plane through the apexes of the two cones. A simple non- self-intersecting quadrilateral is a rhombus if and only if it is any one of the following:  . Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides.
In addition, the square is a special case or type of both the rectangle and the rhombus. Here are the properties of the rhombus, rectangle, and square. Note that because these three quadrilaterals are all parallelograms, their properties include the parallelogram properties. All the properties of a parallelogram apply the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary. All the properties of a parallelogram apply the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other.
A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length, i. The word rhomb is sometimes used instead of rhombus, and a rhombus is sometimes also called a diamond. A rhombus with is sometimes called a lozenge. The polygon diagonals and of a rhombus are perpendicular and satisfy. The diagonals are related to the opening angle by. The rhombus is a tangential quadrilateral with , and so has inradius. Beyer, W. Harris, J. New York: Springer-Verlag, pp.