Last modified on August 3rd, 2023

chapter outline

 

Square vs Rectangle

Square and rectangle are examples of two-dimensional shapes. They both fall under the category of quadrilaterals.

A square is a closed plane figure with four equal sides and four vertices forming four interior right angles. In contrast, a rectangle is a closed plane figure with four straight sides and four vertices forming four interior right angles.

The differences and the similarities between squares and rectangles can be understood if we study their properties. The figure given below shows what distinguishes a square from a rectangle.

Square Vs Rectangle

The differences and similarities in properties are also presented below in a tabular form.

SIDESSQUARERECTANGLE
All sides are equalYesNo
Opposite sides are equal and parallelYesYes
ANGLESSQUARERECTANGLE
All interior angles are equalYesYes
Opposite interior angles are equalYesYes
Sum of two adjacent angles is 180°YesYes
DIAGONALSSQUARERECTANGLE
Bisect each otherYesYes
Bisect perpendicularlyYesNo

Despite the differences, the above table and figure also show how are squares and rectangles alike.

Is a Square a Rectangle

YES. A square can be a rectangle as it follows all the properties of a rectangle. They are given below:

  • Opposite sides are equal and parallel
  • All interior angles are equal
  • Diagonals bisect each other and are equal

Thus a square is considered a special type of rectangle.

Are all Squares Rectangles

YES! Every square is a rectangle because a square satisfies all the properties of a rectangle.

So, what makes a square a special rectangle?

Remember, a rectangle is a closed figure with 4 straight sides and 4 interior right angles. Doesn’t a square also satisfy this definition? YES!

A square is a special type of closed figure with 4 straight sides and 4 right angles that also has all its 4 sides of equal length.

However, imagine the other way round. Is a rectangle a square?

We know a square has all its sides equal, and its diagonals are perpendicular to each other.

Does a rectangle satisfy these added properties that a square exhibits? NO.

A rectangle has its adjacent sides unequal. It does not satisfy the congruency of all its sides which a square does.

Thus, we can conclude that a square is always a rectangle, but a rectangle is not a square.

FAQs

Q.1. When is a rectangle a square?

Ans. Every rectangle with four congruent sides is a square.

Q.2. Why is a rectangle not a square?

Ans. Rectangles do not have all four sides congruent, and the diagonals do not intersect at 90°. So, a rectangle is not a square.

Q.3 Is a square always a rectangle?

Ans. Yes. A square have all the properties of a rectangle and thus is considered a rectangle.

Last modified on August 3rd, 2023

Leave a Reply

Your email address will not be published.