Is Square a Rectangle?
The similarities in the properties of a square and a rectangle can help us draw a conclusion to the query "Is square a rectangle". In Geometry, we have learned about different types of shapes such as square, rectangle, cylinder, rhombus, cuboid, cube, cone, parallelogram, and so on. Many of these shapes share certain common properties. Square and rectangle are examples of such two-dimensional shapes. They both fall under the category of quadrilaterals.
|1.||Square Vs Rectangle|
|2.||Properties of Square and Rectangle|
|3.||What Makes Square a Special Rectangle?|
|4.||FAQs on Is a Square a Rectangle|
Square vs Rectangle
Square: A square is a two-dimensional plane figure with four equal sides, four interior right angles, and four corners. In other words, a square is a quadrilateral or a 4-sided polygon. All the angles are of equal measure, therefore it is considered as an equiangular quadrilateral.
Rectangle: A rectangle is a two-dimensional figure with four sides, four interior right angles, and four corners. The opposites sides of a rectangle are equal. A rectangle has four angles, with each angle measuring 90º. Similar to a square, a rectangle is also referred to as an equiangular quadrilateral.
Let us have a look at the image given here to understand a square and a rectangle better.
Since both a square and a rectangle have an equal number of sides, i.e., 4, we thus can conclude that both square and rectangle are quadrilaterals. We can observe the similarities in the properties of both a square and a rectangle in the following section.
Properties of Square and Rectangle
Both a square and a rectangle have certain special properties that distinguish them from a general quadrilateral. We can draw the comparison of the requisite properties of both the shapes from the following table and conclude whether a square has all the properties that define a rectangle.
How Are Square And Rectangles Alike?
From the comparison drawn above for the common properties shared between a square and a rectangle, we observe that a square has all the properties that define a rectangle, which makes them alike in a certain manner. This means that a square can also be referred to as a type of rectangle.
Thus, we can finally conclude that yes, a square is a rectangle.
What Makes Square a Special Rectangle?
Yes, a square is a special type of rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has:
- interior angles which measure 90∘ each.
- opposite sides that are parallel and equal.
- two diagonals that bisect each other and are equal.
A square is called a special kind of rectangle because it possesses some additional properties which do not apply to rectangles. They are:
- All four sides of a square are equal.
- Diagonals of a square bisect each at right angles.
Given below are a few important notes on the topic is a square a rectangle.
- All squares are rectangles, but not all rectangles are squares.
- All squares are rhombuses, but not all rhombuses are squares.
Try thinking out of the box to answer the following:
- Is every four-sided figure a quadrilateral?
- Are all rectangles squares?
- Are all rhombuses squares?
- Is a square a trapezoid?
- Is a square a parallelogram?
Solved Examples on Is a Square a Rectangle
Example 1: Write a few common properties between squares and rectangles.
We know that a square is a special rectangle. Thus, all the properties of a rectangle will also be the properties of a square. Some of the properties include:
They have four sides.
They have four vertices.
The opposite sides are equal and parallel to each other.
The interior angle at each vertex is 90°.
The diagonals bisect each other.
Example 2: There is a park near Sam's house. The length of the sides of the park is 300 meters, 400 meters, 300 meters, and 400 meters. Determine whether the park is a square or a rectangle.
The length of each side of the park is given as 300 meters, 400 meters, 300 meters, and 400 meters. Now, we know that all four sides of a square are equal. Hence, this is not a square. Given that a rectangle has opposite sides equal, we can see that the given dimensions are of a rectangle, and not a square.
∴ The park is a rectangle.
FAQs on Is Square a Rectangle
Is Square a Rectangle - Yes or No?
The answer is Yes. A square is a rectangle because it possesses all the properties of a rectangle. These properties are:
- Interior angles measure 90∘ each.
- Opposite sides that are parallel and equal.
- Two diagonals that bisect each other and are equal.
What Is the Difference Between Square and Rectangle?
Squares possess some additional properties which do not apply to rectangles. A square has all four sides equal whereas, in a rectangle, only the opposite sides are equal.
Is a Square a Rectangle and a Rhombus?
A square is both a rectangle and a rhombus because it possesses the properties of rectangles and rhombuses. If you are also looking for the answer to the question - is a rhombus a rectangle, the answer is no.
A Square Is a Rectangle. Is This Statement True or False?
This statement is true. A square is a rectangle because it possesses all the properties of a rectangle.
Why Is Square a Special Type of Rectangle?
A square is a special type of rectangle because it possesses all the properties of a rectangle. Similar to a rectangle, a square has interior angles which measure 90º each. opposite sides that are parallel and equal.
Why a Rectangle Is Not a Square?
The rectangle does not necessarily have all four sides of equal measure. This is the reason that rectangle is not a square.