 Probability: Why Is A Square Also A Rectangle

# Probability: Why Is A Square Also A Rectangle

Posted by Madhu Gupta

To know why a square is also called a rectangle, we have to first understand the definition of both the square and rectangle. A square is a parallelogram, whose sides intersect at a 90-degree angle, and a rectangle is also a parallelogram, whose sides intersect at a 90-degree angle. In a rectangle, if the opposite sides of both the pairs are of equal length, then the rectangle can also be called a square. This means we can say that a square is also a rectangle in some cases and a square is indeed a rectangle. The other reasons why a square is also a rectangle are:

• Squares and rectangles are both types of a quadrilateral, and the four interior angles are equal to 90 degrees in both square and rectangle.
• Also, the opposite sides are parallel to each other in the case of squares and rectangles.

So, it is clear that a square is a rectangle, but a rectangle is not a square. All four sides of a square are equal in length, and all four angles in a square are right angles. This is why we can say that a square is also a rectangle. But, in the case of a rectangle, the two horizontal sides are longer than the vertical sides. That means, in a rectangle, the two opposite pairs are parallel. Unlike a square in a rectangle, all four sides are not equal. So, a rectangle is not a square at all.

To understand this concept more elaborately, let’s find out the characteristics of the square and rectangle:-

## Characteristics Of A Square

A square is a four-sided figure where all the sides are equal. And same as a rectangle, all the sides in a square also meet at a 90-degree angle. The other characteristics of a square include:

• The Sides Are Equal: A square has four sides, and all four sides are equal. For example, in a figure, if MN is 6 cm long, then NO, OP and MP will also be 6 cm long on each side.
• The Other Sides Are Parallel: In a square, the opposite sides are always parallel. For example, in a figure, MN and PO are parallel to each other, and NO and MP are also parallel to each other.
• All The Four Angles Are Right Angles: All the four angles in a square are right angles, which means mean it is 90 degrees. For example, in a figure, ∠MNP, ∠NOP, ∠OPM, and ∠PMN, each of these angles is 90 degrees.
• The Adjoining Angles Are Supplementary: The adjoining angles in a square are always supplementary. That means if we add these adjacent angles, it will be 180 degrees. For example, in a figure, when we add up adjacent angles ∠NMP and ∠MPO, it will be 180 degrees, as they are adjoining angles.
• Equal Diagonals: Diagonals are always equal in a square. For example, in the same figure of a square, NP and MO, both are of equal length.
• Equal Diagonals are Perpendicular Bisectors:  In a square, the diagonals bisect each other at 90-degree angles, so they are called perpendicular bisectors. For example, in the same figure, the equal diagonals NP and MO both intersect at point R, and they both bisect each other at 90-degree angles, so they are also called perpendicular bisectors.

## Characteristics Of A Rectangle

A rectangle is a four-sided two-dimensional figure. In a rectangle, there are four straight lines, and these straight lines make a 90-degree angle. The other characteristics of a rectangle are:-

• Opposite Two Sides Are Parallel: The opposite two sides of a rectangle are always parallel. For example, in a figure of a rectangle, MP and NO are parallel, while MN and PO are also parallel.
• Opposite Two Sides Are Equal: The opposite two sides of a rectangle are always equal. For example, in a figure of a rectangle, if MP is 6 cm long, then its opposite side, NO, is also 6 cm long.
• All The Four Angles Are Right Angles: All the four angles in a rectangle are right angles, which means it is 90 degrees. For example, in a figure of a rectangle, ∠MNP, ∠NOP, ∠OPM, and ∠PMN, each of these angles is 90 degrees.
• The Adjoining Angles Are Supplementary:  Like a square is a rectangle, also the adjoining angles are always supplementary. That means if we add these adjacent angles, it will be 180 degrees. For example, in a figure rectangle, when we add up adjacent angles ∠NMP and ∠MPO, it will be 180 degrees, as they are adjoining angles.
• Equal Diagonals: Diagonals are also equal in a rectangle, like a square. For example, in the same figure as a rectangle, NP and MO both are of equal length.
• Intersect Diagonals Bisect Each Other: When we divide a line into two halves, then it is called bisecting. And in the case of a rectangle, these diagonals will intersect at a point where they will bisect each other. For example, in the same figure as a rectangle, MO and NP intersect at B, and it divides the diagonals into two halves. Hence, if MO and NP are 6 cm each, then MB, PB, OB, and NB are all 3 cm each.

Since we have now understood the concept of a square and rectangle more elaborately, we can get an idea about why a square is also called a rectangle. Because of some of the similarities between a square and a rectangle, we can call a square a rectangle. But you always have to remember one thing that a rectangle is not a square. The reasons why a rectangle is not a square are:

• All four angles of a rectangle are 90 degrees, but it is not a square because, in a rectangle, the two horizontal sides are longer than the vertical sides. That means in a rectangle. The two opposite pairs are parallel. But in the case of a square, all four sides are equal and parallel. This is the fundamental difference between a rectangle and a square, and that is why a rectangle is not a square at all.

## Conclusion

Squares and rectangles are important topics in Geometry. These are the basic concepts of shapes that are necessary for you to learn at your school level. Along with squares and rectangles, there are also some other shapes in Geometry, such as a cube, cylinder, rhombus, cone, parallelogram, and many more. All these shapes fall under two-dimensional shapes and three-dimensional shapes categories. The characteristics and properties of all these shapes are different.

In this article, we give you a very clear idea about the concept of squares and rectangles. Now, you may be able to know why a square is also a rectangle and why a rectangle is not a square. What are the characteristics and differences between a square and a rectangle? To learn such types of similar topics online, you can enroll your kids in Cuemath. During this pandemic, every parent wants to offer the best online education to their kids and the best practice on mathematics for younger kids. Cuemath is the best and trusted educational website.

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