Theory:

A parallelogram with all sides are equal is called a rhombus.
Now we are going to define a rhombus \(ABCD\) as a quadrilateral is a parallelogram with all the sides are in equal measures.
 
EX_12_1.png
 
Thus, if \(ABCD\) is a rhombus then \(AB = BC = CD = AD\), \(AB || CD\) and \(BC || AD\).
 
Important!
Rhombus is a special case of kite. Note that the sides of a rhombus are all of the same length; this is not the case with the kite.
 
A rhombus has all the properties of a parallelogram and also that of a kite.
In a rhombus, the following properties are true:
  1. The sum of all the four angles of the rhombus is equal to \(360°\).
  2. The opposite sides are equal in length.
  3. The opposite angles are equal in measure.
  4. The adjacent angles are supplementary.
  5. The diagonals are perpendicular bisector of each other.