Difference between Square and Rhombus

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.

Square vs Rhombus

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

Differences

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) = a2 ,here a = side Perimeter (P) = 4a	Area (A) = (d1 × d2)/2, here d1 and d2 are the diagonals Perimeter (P) = 4s ,here s = side

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

Similarities

1. Quadrilaterals
2. Diagonals are mutually perpendicular bisectors
3. The Sum of interior angles is 360°
4. Opposite sides are parallel
5. All sides are equal in length

Is a Square a Rhombus

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.