Rhombus

A parallelogram in which a diagonal bisects an interior angle

Specifications

• a parallelogram in which a diagonal bisects an interior angle
• a parallelogram in which at least two consecutive sides are equal in length
• a parallelogram in which the diagonals are perpendicular (an orthodiagonal parallelogram)
• 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 quadrilateral ABCD possessing a point P in its plane such that the four triangles ABP, BCP, CDP, and DAP are all congruent
• a quadrilateral ABCD in which the incircles in triangles ABC, BCD, CDA and DAB have a common point

Facts

Area:
\displaystyle K=a^{2}\cdot \sin \alpha =a^{2}\cdot \sin \beta (Based on sin of angle)

Equation:
\displaystyle \left|{\frac {x}{a}}\right|\!+\left|{\frac {y}{b}}\right|\!=1