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 that I do not know the area and perimeter properties.)
The 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 .
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, a rhombus follows some of the rules that a parallelogram does. The following properties 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.