Properties

A rhombus is a parallelogram with four congruent sides.

RhomDef

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.

  • Each diagonal bisects a pair of opposite angles.

RhomProp1

Remember opposite angles in a parallelogram are congruent.  Therefore, it can be proven that all 4 angles created by the diagonal are congruent.

  • The diagonals are perpendicular.

RhomProp2

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.

 

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