Difference Between Rectangle and Parallelogram
In geometry, we have set quadrilaterals, two-dimensional shapes with four sides, four angles, and four vertices. Rectangles and parallelograms are among the common shapes seen around us. However, they seem to have a few common properties, but they have a few other properties that mark the point of differences between them. The main difference between them is that a parallelogram has opposite sides equal, while in a rectangle, the opposite sides are equal with all its adjacent sides being perpendicular to each.
What is a Rectangle and a Parallelogram?
Although rectangles and parallelograms are quadrilaterals, there are certain properties that differentiate them.
A rectangle is a two-dimensional shape. It has four equal vertices and the interior angles formed at the vertices are all equal. All the four angles of a rectangle measure 90°. It is also called a parallelogram as its opposite sides are parallel.
A parallelogram is also a two-dimensional shape. It has four vertices. The interior angles formed at the vertices are such that the adjacent angles add up to make supplementary angle pairs. A quadrilateral is referred to as a parallelogram if its opposite sides are parallel and congruent.
Properties of a Rectangle and a parallelogram
Some important properties of a rectangle are:
- The opposite sides of a rectangle are equal as well as parallel to each other.
- All the internal angles of a rectangle are right angles, each measuring 90°.
- The opposite angles of a rectangle are equal.
- The diagonals of a rectangle are of the same measure and bisect each other.
Some important properties of a parallelogram are:
- The opposite sides of a parallelogram are equal as well as parallel to each other.
- The same-side interior angles of a parallelogram supplement each other.
- The opposite angles of a parallelogram are equal.
- The diagonals of a parallelogram bisect each other.
Difference Between a Rectangle and a Parallelogram
The important differences between a rectangle and a parallelogram are listed in the table given below.
Rectangle vs Parallelogram
|Sides||The opposite sides are equal.||The opposite sides are equal.|
|Diagonals||The unequal diagonals of a parallelogram bisect each other.||The equal diagonals of a rectangle bisect each other at different angles.|
The opposite angles of a parallelogram are equal.
The adjacent angles are supplementary.
Opposite angles, as well as adjacent angles, are equal.
An angle formed by the adjacent sides of a rectangle is 90°.
Rectangle and Parallelogram Formulas
Once we know the length of the sides and the length of the diagonals of a given square and a rhombus, we can use the following formulas to calculate their area and perimeter.
- The formula for the area of a rectangle is: Area of a rectangle = l × b, where 'l' is the length of the rectangle and 'b' is the breath of the rectangle.
- The formula for the perimeter of a rectangle is: Perimeter of a rectangle = 2 (l + b), where 'l' is the length of the rectangle and 'b' is the breath of the rectangle.
- The formula for the area of a parallelogram is: Area of a parallelogram = b × h, where 'b' is the length of the base of the parallelogram and 'h' is the height of the parallelogram.
- The formula for the perimeter of a parallelogram is: Perimeter of a parallelogram = 2 (a + b), where 'a' and 'b' are the adjacent sides of the parallelogram.
Is Rectangle a Parallelogram?
A rectangle is a special parallelogram having the following properties.
- Two pairs of parallel sides.
- Four right angles at four vertices.
- Opposite sides of equal lengths.
- Two equal diagonals bisecting each other.
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Examples on Difference Between a Rhombus and a Rectangle
Example 1: Determine the properties of a rectangle that are not similar to that of a parallelogram.
In a rectangle,
- the opposite sides are equal with all its adjacent sides being perpendicular to each other.
- four interior angles, each equal to 90°.
- the diagonals are equal or of the same measure.
Example 2: Calculate the area of a rectangle with the dimensions 8 units and 5 units.
The formula used to calculate the area of a rectangle is: area = l × b, where 'l' is the length of the rectangle and 'b' is the breadth of the rectangle.
Given, length = 8 units, breadth = 5 units . Substituting the values in the formula:
Area = l × b = 8 × 5
= 40 square units
Therefore, the area of the given rectangle is 40 square units.
FAQs on Difference Between Rectangle and Parallelogram
What Is the Difference Between Rectangle and Parallelogram?
The important points of differences between a rectangle and a parallelogram:
- A parallelogram has opposite sides equal, while in a rectangle, the opposite sides are equal with all its adjacent sides being perpendicular to each other.
- The diagonals of a rectangle are equal whereas the diagonals of a parallelogram are not equal.
What Are the Similarities Between Rectangle and Parallelogram?
A rectangle and a parallelogram have the following similarities:
- equal and parallel opposite sides.
- equal opposite internal angles.
- supplementary adjacent angles.
What Property of Rectangle Is Different from the Property of Parallelogram?
The property of a rectangle that makes it different from a parallelogram is as follows: All the internal angles of a rectangle are equal to 90 degrees.
How Are Rectangle and Parallelogram Different in Terms of the Diagonals?
Rectangles and parallelograms are different in terms of the diagonals as: The diagonals of a rectangle are equal in measure but it is not so in the case of a parallelogram.
What Are the Important Properties that Confirm That a Rectangle is a Parallelogram?
The properties listed below confirm that a rectangle is a parallelogram:
Since two right angles add to a straight angle, thus we can say that each pair of co-interior angles are supplementary and thus the opposite sides are parallel. Therefore, it can be concluded that opposite sides are equal and parallel, which marks that the given figure is a parallelogram. Also, its diagonals bisect each other.
Can a Parallelogram be a Rectangle?
Both, rectangle as well as parallelograms have their opposite sides equal and parallel. The main point of difference between the two is that sides of rectangles form 90 degrees while this is not the case with parallelograms. Thus, a rectangle can be called a parallelogram as it fulfills all the requirements of a parallelogram but a parallelogram cannot be called a rectangle.