Is a Square a Rectangle?
The answer to the question is yes! All squares are rectangles!
A rectangle and a square are both quadrilaterals. A quadrilateral is a polygon with four sides, four vertices, and four angles. In this article, let’s try to understand why all squares are also considered as rectangles.
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What Is the Shape of a Rectangle and Square?
Rectangle and square are two-dimensional, flat-shaped, closed geometric figures.
Why Is a Square a Special Type of Rectangle?
Let’s learn the definitions of a square and a rectangle and check if a square fits into the definition of a rectangle.
Definition of Rectangle: A rectangle is a quadrilateral with four right angles. For a quadrilateral to be a rectangle, all four interior angles should measure 90.
Definition of Square: A square is a quadrilateral with four right angles and four equal sides.
Since a square has four right angles, it is a rectangle! A square follows all the properties of a rectangle and also has some unique properties of its own.
The key difference between a square and a rectangle is, all sides of a square are equal, whereas only opposite sides of a rectangle are equal.
Rectangle vs. Square
| Rectangle | Square |
|---|---|
| A quadrilateral with four right angles. | A quadrilateral with four right angles. |
| Opposite sides are equal. The longer side measurement is called length. The shorter side measurement is called breadth. | All sides are equal in length. |
| Diagonals bisect each other. | Diagonals bisect each other at right angles. |
| Diagonals are not perpendicular. | Diagonals are perpendicular. |
| Diagonals are equal. | Diagonals are equal. |
| A rectangle is an irregular polygon. | A square is a regular polygon. |
Properties of Square and Rectangle
| Property | Rectangle | Square |
|---|---|---|
| Sides | Opposite sides are equal. | All sides are equal. |
| Opposite sides are parallel. | ||
Angles | All angles are right angles. | |
| Opposite angles are equal. | ||
Diagonals | Diagonals are not perpendicular. | Diagonals are perpendicular. |
| Diagonals bisect each other. | ||
| Diagonals are equal. | ||
On comparing the common properties shared between a square and a rectangle, we observe that a square has all the properties that a rectangle has. In other words, we can say that a square can also be referred to as a special type of a rectangle.
Hence, we can conclude that yes, a square is a rectangle.
How Are Squares And Rectangles Alike?
Properties shared by squares and rectangles:
- Four interior angles each equal to 90 degrees.
- Opposite sides are parallel and equal.
- Two diagonals are equal.
- Diagonals bisect each other.
What Additional Properties Distinguish a Square from a Rectangle?
A square has its own unique properties which a rectangle does not have. These properties are
- All four sides of a square are equal.
- Diagonals of a square bisect each at right angles.
Facts about “Is a Square a Rectangle?”
- A square meets the criteria for being classified as a rectangle, making it a unique type of rectangle.
- All squares are rectangles, but not all rectangles are squares.
- Area of a square = (side)2
- Area of a rectangle = length × breadth
- Perimeter of a square = side + side + side + side = 4 side
- Perimeter of a rectangle = length + length + breadth + breadth = 2 × (length + breadth)
Conclusion
In this article, we explored how a square is a special kind of rectangle. We learned the difference, similarities, and comparison points with properties. Let’s solve a few examples and MCQs for better understanding.
Solved Examples on “Is a Square a Rectangle?”
1. What properties are common in both rectangle and square?
Solution:
Both rectangle and square have the following common properties:
- All angles are equal and are of 90° each.
- The opposite sides of both the rectangle and square are parallel and equal.
- The diagonals of both the rectangle and square are equal.
2. When does a rectangle become a square?
Solution:
The key difference between a square and a rectangle is, all sides of a square are equal, whereas only opposite sides of a rectangle are equal.
A rectangle becomes a square when its length equals its breadth. This way all sides become equal in length.
4. A square is formed by joining lengths of two rectangles as given below. What will be the area of the square?
Solution:
Side of the square = Sum of widths of the two rectangles
Side of the square = a + b
Area of the square = side ✕ side
= (a + b) ✕ (a + b)
= a2 + 2ab + b2 square units.
5. A rectangle is divided into two squares given below. What will be the perimeter of the rectangle?
Solution:
Length of rectangle (l) = (a + b) units
Breadth of rectangle (b) = c units
Perimeter of the rectangle = 2(l + b)
Perimeter of the rectangle = 2(a + b + c) units
Practice Problems on “Is a Square a Rectangle?”
Is a Square a Rectangle? Definition, Facts, Examples, FAQs
Which of the following is NOT true about a square?
Square is a special type of a rectangle. All squares are rectangles.
Which of the following is NOT a common property of squares and rectangles?
The diagonals of a rectangle do not bisect each other at 90°.
The two dimensions of a quadrilateral are 5 inches and 2 inches. Which could be this quadrilateral?
A rectangle has opposite sides equal. So, there is a possibility that the length are 5 inches and breadth is 2 inches.
Are all squares rectangles?
All squares are rectangles.
Frequently Asked Question on “Is a Square a Rectangle?”
Is a square a rhombus?
Squares are quadrilaterals with 4 congruent sides. Since rhombuses are quadrilaterals with 4 congruent sides, squares are by definition also rhombuses.
Is a rectangle always a square?
No. Not every rectangle is a square. To be a square, all sides of a rectangle must have the same length.
Every rectangle is a parallelogram. True or False?
True. A parallelogram in which all the angles are equal is called a rectangle. So, all rectangles are parallelograms. Every rectangle is a parallelogram, but not every parallelogram is a rectangle.
Is rhombus a square?
No. All rhombus are not squares. For a rhombus to be a square, all angles should be right angles. A square is a rhombus, but a rhombus is not necessarily a square.
Is rhombus a special type of rectangle?
No, rhombus is not a special type of rectangle as rhombus does not have all properties of a rectangle.
Why is a rectangle not a regular polygon?
A rectangle is not a regular polygon since all sides are not equal. It is only an equiangular polygon.
Is every square a rectangle?
Yes, every square is a rectangle.
