Diagonals of a Rhombus

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.

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.

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

If ABCD is a rhombus, find BC and BD. AD = 5, PC = 3.

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.