[Maths Class Notes] on Difference Between Square and Rectangle Pdf for Exam

You might have heard of the shapes: square and rectangle. In fact, if you look around, you are surrounded by squares and rectangles. But you might ask: What is the difference between a square and a rectangle? Visually, they might look similar. Both rectangles and squares have four straight sides. However, mathematically, the properties of a square and a rectangle are quite different. For example, a common difference is that squares have all equal sides while in a rectangle, only the opposite sides are equal. 

 

A similarity between rectangles and squares is that they are both 2-dimensional figures. To understand the difference between square and rectangle, we need to first understand the concept of two dimensional shapes. In geometry, we generally deal with two-dimensional and three-dimensional shapes.

 

What Are Two Dimensional Shapes?

A two-dimensional shape is defined as a flat figure. It is a plane figure which generally has two measurements: length and breadth. These figures do not have thickness or depth. For example, a paper sheet is two dimensional in shape and has a length and width but does not have height and depth. There are many different types of 2-D figures like rectangle, square, circle, hexagon and triangle. Both square and rectangle are two-dimensional shapes having length and breadth only.

 

2D figures can have different characteristics which can help us differentiate and define each shape separately. Both square and rectangle have different characteristics which help us differentiate between the two. 

 

What Is A Rectangle?

A rectangle is a two-dimensional figure with four sides. A rectangle is made of four straight lines that make a 90-degree angle. It is referred to as a quadrilateral. A quadrilateral is a plane figure with four sides. It has four angles, four sides and four vertices (the points where the edges meet). The figure below shows a rectangle with vertices A, B, C and D. The sides are AD, DC, CB and BA while the diagonals are AC and DB. The diagonals intersect at R.

 

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What are the Characteristics of a Rectangle?

1.  Opposite Sides are Parallel: 

Any two opposite sides of a rectangle will be parallel. In the above case, AD and BC are parallel while AB and DC are parallel.

2. Opposite Sides are Equal: 

The opposite sides of a rectangle are equal. In the figure, if AD is 5cm long, then the opposite side, i.e., BC is also 5cm long. 

3. All the Angles are Right Angles, i.e., 90 Degrees: 

In a rectangle, the angles formed by the sides are right angles. Hence, there are a total of four 90-degree angles. So ∠ADC,∠DCB, ∠CBA and ∠BAD are 90 degrees each. 

4. Adjacent Angles are Supplementary:

Adjacent means a pair of angles which form on the same side of a straight line especially when one side is meeting or intersecting with another line. Adjacent angles of a rectangle are supplementary i.e., they add up to 180 degrees.

5. Diagonals are Equal: 

Diagonals are straight lines which are drawn from one corner to the opposite corner. In the figure, BD and AC are the diagonals and are of the same length.

6. Diagonals Bisect Each Other: 

The diagonals of a rectangle will intersect at a point where they will bisect each other. Bisecting means dividing a line into two equal halves. In the figure, AC and BD intersect at R, which divides the diagonals into halves. So, if AC and BD are 8cm each, AR, DR, CR and BR are all 4cm each.

 

What is a Square?

A square is a quadrilateral with four sides. All of these four sides are equal. Similar to the rectangle, all the sides of a square meet at 90-degree angle. Let us look at the figure below:

 

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Here, there are four sides – AB, BC, CD and DA. The diagonals, in this case, are AC and BD. 

 

What Are The Characteristics of a Square?

1. Opposite Sides are Parallel: 

In the above figure, AB and CD are parallel, while BC and AD are parallel to each other. In a square, opposite sites are always parallel. 

2. All Sides are Equal: 

All sides of a square are equal. For example, if AB is 5cm long, BC, CD and AD will also be 5cm long each.

3. All the Angles are Right Angles: 

In a square, the angles formed by the sides are right angles. In the above figure, each of the angles – ∠ABC, ∠BCD, ∠CDA and ∠DAC are 90 degrees each.

4. Adjacent Angles are Supplementary: 

In squares, adjacent angles are supplementary, i.e., they add up to 180 degrees. So in the above figure, for example, ∠BAD and ∠ADC angles add up to 180 degrees as they are adjacent angles. 

5. Diagonals are Equal: 

The diagonals of a square are equal to one another. In this case, the diagonals are BD and AC – which are both of equal length in squares. 

6. Diagonals are Perpendicular Bisectors: 

The diagonals BD and OC intersect at point O. For squares, they bisect each other at 90-degree angles, i.e., they are perpendicular bisectors. 

 

You might wonder what the difference between rectangle and square is? Essentially, there are two basic differences when we compare square vs rectangle.

 

What is the Difference Between a Rectangle and a Square?

The square and rectangle are also two-dimensional shapes which have 4 sides but slightly differ in some properties.  

 

This is the basic difference between a rectangle and a square.

 

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