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Rhombus And Parallelogram both shapes share some similarities but also have distinct characteristics. Both rhombus and parallelogram are types of quadrilaterals, which means they are four-sided polygons. However, a key difference lies in the properties of their sides and angles.
A parallelogram is defined as a quadrilateral where opposite sides are parallel and equal in length, whereas a rhombus is a special type of parallelogram where all four sides are of equal length. In this article, we will explore the fundamental differences between a rhombus and a parallelogram, two commonly studied quadrilaterals in geometry.
 What is Quadrilateral?Quadrilateral is the closed shape and one type of polygon having four sides, four vertices & four angles. Its formed by taking four no collinear points.
The term quadrilateral comes from the Latin origins ‘Quadra’ which means four and ‘Latus’, meaning sides. Interior angles of quadrilaterals add to 360°. Examples of Quadrilaterals include parallelogram, trapeziums, rectangle, squares, etc.
In this article, we will discuss rhombus as well as parallelograms including their differences.
What is Rhombus?A quadrilateral, all of whose four sides are equal in length is called a rhombus.
Equal sides make it a special diamond shape. Rhomboid is one of those special kinds, with symmetry properties and equal sides making it a unique shape as well an important item either for understanding geometric properties or used in real applications like design & architecture.
Properties of RhombusSome of the common properties of rhombus are:
- All four sides of a rhombus are of equal length.
- The opposite angles of a rhombus are equal to each other.
- The sum of any two adjacent angles in a rhombus is 180 degrees.
- The diagonals of a rhombus intersect at 90 degrees (right angles).
- The diagonals of a rhombus not only intersect at right angles but also bisect the angles of the rhombus.
- A rhombus has two lines of symmetry, which are its diagonals. It also has rotational symmetry of order 2.
- A square is a special case of a rhombus where all the angles are right angles (90 degrees).
What are Parallelogram?A parallelogram is a type of quadrilateral characterized by having two pairs of opposite sides that are both parallel and equal in length.
Parallelograms are used extensively in engineering, and physics with the mediation of forces or vectors. They are also used in computer graphics for modeling shapes and transformations (like rotating or moving something).
Properties of ParallelogramSome of the common properties of parallelograms are:
- In a parallelogram, each pair of opposite sides is parallel and of equal length.
- The angles opposite each other in a parallelogram are equal.
- Any two adjacent angles in a parallelogram add up to 180 degrees.
- The diagonals of a parallelogram intersect at their midpoints, meaning they bisect each other.
- The angles between two adjacent sides of a parallelogram are supplementary.
- Rectangles, rhombuses, and squares are all special types of parallelograms.
Read More about Parallelograms.
Difference Between Rhombus and ParallelogramSome of the common differences between rhombus and parallelogram are:
Feature
| Rhombus
| Parallelogram
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Definition
| A rhombus is a quadrilateral with all sides of equal length.
| A quadrilateral is a parallelogram with opposite sides that are parallel and equal in length.
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Sides
| It has four sides and all the sides are of equal length.
| It has also four sides but only opposite sides are equal in length.
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Diagonals
| Diagonals of rhombus bisect each other at right angles and are not equal in length.
| Parallelogram diagonals bisect each other but are not necessarily at right angles.
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Opposite Angles
| Its opposite angles are equal.
| Its opposite angles are also equal.
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Symmetry
| It has two lines of symmetry along its diagonals.
| Generally it does not have lines of symmetry unless it is a special case like a rectangle or square.
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Special Cases
| A special type of parallelogram with all sides equal and perpendicular diagonals.
| A general category that includes rhombuses, rectangles, and squares.
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Area Formula
| [Tex]\text{Area of Rhombus} = \frac{1}{2} \times d_1 \times d_2[/Tex]
Where d1 and d2 are diagonals
| [Tex]\text{Area} = \text{base} \times \text{height}
[/Tex]
Where base is the length of one side, & height is perpendicular distance between base and opposite side.
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Perimeter Formula
| [Tex]\text{Perimeter of Rhombus} = 4 \times \text{Side Length} [/Tex]
| [Tex]\text{Perimeter} = 2 \times (\text{length} + \text{width})[/Tex]
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Diagonals Intersection
| Intersect at right angles (90 degrees).
| Bisect each other without necessarily forming right angles.
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Consecutive Angles
| Sum of consecutive angles of rhombus are 180 degrees i.e. supplementary.
| Sum of consecutive angles of parallelogram are 180 degrees i.e. supplementary.
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Applications
| Used in design, architecture, tiling patterns, and kite construction.
| Used in engineering, physics (study of forces and vectors), and computer graphics.
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Read More,
FAQs: Rhombus And ParallelogramDescribe one common difference between a rhombus and parallelogram.All four sides are equal in a rhombus, and only parallel sides of the parallelogram need to be equivalent(commutative). This definition sets a rhombus apart from any other type of parallelogram, and helps to identify some unique properties of its own.
Is a Rhombus a Parallelogram?Yes, a rhombus is a parallelogram but not all the rhombuses are parallelograms.
Is a square also a rhombus or a parallelogram?A square is a special type of rhombus (with diagonals) and furthermore an extraordinary kind of parallelogram (all sides equivalent and right angles). So a square is both types of shapes, with extra characteristics.
To what real-life situation you can relate rhombuses & parallelograms?Rhombuses are used among other things in design and architecture, whereas parallelograms form the basis of cross-disciplinary models such as those found naturally or sometimes imitated by man including trapezoids.
How to prove that a quadrilateral is rhombus?To prove a quadrilateral as a rhombus, all four sides of a quadrilateral must be of same length and also their diagonals should intersects each other at right angles i.e. 90 degrees. Properties that makes a figure certain to be rhombus.
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