A rhombus is a parallelogram with four congruent sides.
Because it is a parallelogram, all of the properties of a parallelogram apply to the rhombus. Therefore, in a rhombus, opposite angles are congruent, consecutive angles are supplementary and its diagonals bisect each other.
There are two properties that are special to a rhombus.
Remember opposite angles in a parallelogram are congruent. Therefore, it can be proven that all 4 angles created by the diagonal are congruent.
The perpendicular diagonals create right triangles that can be proven congruent using the properties already introduced. Take a moment to consider which triangles are congruent and why.
*Note: All rhombuses are parallelograms, but not all parallelograms are rhombuses.
All of the properties that apply to a rhombus, can be used to find unknown quantities. Be careful when determining which one to use.