# Diagonals of a Rhombus

How to solve the diagonals of a rhombus problems: property, example, and its solution.

## Definition

A rhombus is a parallelogram

whose sides are all congruent.

So a rhombus has all the properties of a parallelogram.

## Property

The diagonals of a rhombus

perpendicularly bisect each other.

Recall that the diagonals of a parallelogram

just bisect each other.

(not perpendicularly bisecting each other.)

## Example

The sides of a diagonal are all congruent.

So *AD* = *BC* = 5.

(brown)

See △*PBC*.

Its hypotenuse is 5.

And its leg is 3.

So it's a (3, 4, 5) triangle.

So *PB* = 4.*BD* is perpendicularly bisected by *AC*.

So *DP* = *PB* = 4.

And *BD* = 4 + 4.