## 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.**

#### Begin here

## What Is the Shape of a Rectangle and Square?

Rectangle and square are two-dimensional, flat-shaped, closed geometric figures.

#### Related Worksheets

## 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 + b^{2} 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.