Table of Contents

Last modified on August 3rd, 2023

Both squares and rhombuses are special parallelograms.

**A square **is a quadrilateral with 4 equal sides and 4 interior right angles.

**A rhombus **is a quadrilateral with 4 equal sides with 2 pairs of parallel opposite sides and equal opposite angles.

Although squares and rhombuses are parallelograms, they have some differences. Let us learn how a rhombus is different from a square.

Basis | SQUARE | RHOMBUS |
---|---|---|

Sides | Adjacent sides are perpendicular to each other | Adjacent sides are not perpendicular to each other |

Interior angles | All the angles are equal All angles are right angles | Only the opposite angles are equal All angles are not right angles |

Diagonals | Equal | Unequal |

Lines of symmetry | 4 lines of symmetry | 2 lines of symmetry |

Inscription in a circle | It can be inscribed in a circle | It cannot be inscribed in a circle |

Formulas | Area (A) = a^{2} ,here a = sidePerimeter (P) = 4a | Area (A) = (d_{1} Ã— d_{2})/2, here d_{1} and d_{2} are the diagonalsPerimeter (P) = 4s ,here s = side |

Besides the differences, they also share some similarities as given below:

- Quadrilaterals
- Diagonals are mutually perpendicular bisectors
- The Sum of interior angles is 360Â°
- Opposite sides are parallel
- All sides are equal in length

YES. A square is a rhombus.

A square satisfies all the properties of a rhombus.

A square has 4 equal sides. It has equal diagonals that are perpendicular bisectors. The opposite sides of a square are equal and parallel and the opposite angles are also equal.

So, **is a square always a rhombus?**

YES. A square is also a rhombus because it will always have 4 interior right angles as a fixed property. So every square is a rhombus.

Now let us think the other way round. **Is a rhombus a square?**

NO. Then what is the difference between a square and a rhombus?

The key difference between a square and a rhombus is that the interior angles of a rhombus may vary. Thus, a rhombus is not always a square.

So **when is a rhombus a square?**

Every rhombus with four right angles is a square.

Therefore, all squares are rhombuses, but all rhombuses are not squares.

Last modified on August 3rd, 2023