A rhombus is a parallelogram in which all sides are equal. It's much more basic than a parallelogram and has the opposite properties of a rectangle. (I do not have all the properties, and information on this subject since I am in a college prep geometry class, so I would appreciate it if someone would add information and review my work) (Note - I do not know the the area & perimeter properties)
The following definition of a rhombus is as follows.
A rhombus is a quadrilateral whose sides are all equal.
Notice that the diagonals are perpendicular and the sum of the perpendicular angles is \( 360^\circ \).
Property 1. All pairs of the consecutive sides of a rhombus are congruent
Property 2. The diagonals of a rhombus are perpendicular
Remember, if a quadrilateral is both a rectangle and a rhombus, then it is a square.
Since all rhombuses are parallelograms, but not all parallelograms are rhombuses the rhombus follows some of rules that a parallelogram does. The following properties below apply to parallelograms and rhombuses:
Property 3. One diagonal of a rhombus bisects a pair of opposite angles
Property 4. The opposite sides of a rhombus are parallel.