# Rhombus vs Parallelogram

Rhombuses and parallelograms both belong to the family of quadrilaterals. All types of quadrilaterals have some properties that bring them under the same category. However, each member of the family is different from the other in some aspects. Here we will discuss the differences between a rhombus and a parallelogram.

Let us compare the figure of a rhombus and a parallelogram below.

## Similarities Between a Rhombus and a Parallelogram

• Have four sides
• Opposite sides equal and parallel
• Opposite angles equal
• Diagonals bisecting each other

## Is a Rhombus a Parallelogram

YES! Remember, a parallelogram has 2 pairs of sides that are mutually opposite, parallel, and equal, and 2 diagonals mutually bisecting. Doesn’t a rhombus also satisfy this definition? YES. A rhombus satisfies all the properties of a parallelogram. So a rhombus is a parallelogram. Therefore, we can consider a rhombus as a subset of a parallelogram.

However, is a rhombus always a parallelogram?

YES! A rhombus is always a parallelogram.

A rhombus exhibits all the properties of a parallelogram. Also, it has all its sides congruent. Its all-sides congruency makes the diagonals bisect perpendicularly. Thus, we often consider a rhombus as a slanting square and a parallelogram as a slanting rectangle.

## How to Prove a Parallelogram is a Rhombus

To prove: ABCD is a rhombus

Proof:

Given: ABCD is a parallelogram