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103 LearnersLast updated on September 3, 2025
Properties of a Rhombus
A rhombus is a type of quadrilateral that has many unique properties. These properties help students simplify geometric problems related to rhombuses. The properties of a rhombus include having all sides equal in length, and its diagonals bisect each other at right angles. These properties help students analyze and solve problems related to symmetry, angles, and area. Now let us learn more about the properties of a rhombus.
What are the Properties of a Rhombus?
The properties of a rhombus are simple, and they help students to understand and work with this type of quadrilateral. These properties are derived from the principles of geometry. There are several properties of a rhombus, and some of them are mentioned below:
Property 1: Equal Sides
All four sides of a rhombus are equal in length.
Property 2: Opposite Angles
The opposite angles of a rhombus are equal.
Property 3: Diagonals
The diagonals of a rhombus bisect each other at right angles. Furthermore, each diagonal bisects a pair of opposite angles.
Property 4: Symmetry
A rhombus has two lines of symmetry along its diagonals.
Property 5: Area
Formula The formula used to calculate the area of a rhombus is given below: Area = ½ × d1 × d2 Here, the lengths of the diagonals are represented as d1 and d2.
Tips and Tricks for Properties of a Rhombus
Students often confuse and make mistakes while learning the properties of a rhombus. To avoid such confusion, we can follow the following tips and tricks:
Equal Sides: Students should remember that in a rhombus, all sides are equal in length. To verify this, they can draw a rhombus and measure the sides to see that they are equal.
Diagonals are Perpendicular: Students should remember that the diagonals of a rhombus always intersect at right angles.
Diagonals Bisect Angles: Students should remember that in a rhombus, each diagonal bisects a pair of opposite angles.
Confusing a Rhombus with a Square
Students should remember that while both a rhombus and a square have all sides equal, a square has all angles equal to 90 degrees, whereas a rhombus does not necessarily have right angles.
Mistake 1
Misinterpreting the Diagonal Relationship
Students should know and remember that the diagonals of a rhombus bisect each other at right angles and that they also bisect the opposite angles.
Mistake 2
Incorrectly Applying the Formula
Students should practice the formula used to find the area of a rhombus, which is given below. They must also understand the representations of d1 and d2. Area = ½ × d1 × d2
Mistake 3
Misunderstanding Angle Relationships
Students should remember that the opposite angles of a rhombus are equal. This means if one angle is known, the opposite angle is the same.
Mistake 4
Forgetting the Equal Side Rule
Students must remember that a rhombus has all four sides equal in length.
Mistake 5
Solved Examples on the Properties of Rhombuses
In a rhombus, the four corners are marked as A, B, C, and D. If AB = 5 cm, what are the lengths of the other sides?
BC = 5 cm, CD = 5 cm, DA = 5 cm.
Problem 1
In a rhombus, all sides are equal. Since AB = 5 cm, then BC = CD = DA = 5 cm.
In a rhombus ABCD, the angle ABC = 120 degrees. What is the measure of angle ADC?
Explanation
ADC = 120 degrees
Problem 2
In a rhombus, the opposite angles are equal. Here, the angles ABC and ADC are opposite. Hence, angle ADC = 120 degrees.
The diagonals of a rhombus intersect at point O. If angle AOB = 90 degrees, what can you conclude about the diagonals of the rhombus?
Explanation
Diagonals of the rhombus are perpendicular to each other.
Problem 3
The angle AOB is 90 degrees. According to a property of rhombuses, the diagonals of a rhombus are perpendicular to each other.
In rhombus ABCD, diagonal AC bisects diagonal BD at point E. If BE = 4 cm, what is the length of ED?
Explanation
ED = 4 cm
Problem 4
Since BE = 4 cm and the diagonals of a rhombus bisect each other, then ED = BE = 4 cm.
A rhombus has diagonals of length 12 cm and 16 cm. What is the area of the rhombus?
Explanation
Area = 96 sq cm.
A rhombus is a quadrilateral with all four sides equal in length and its diagonals bisecting each other at right angles.
1.How many pairs of equal sides does a rhombus have?
2.Are all angles of a rhombus equal?
3.How do you find the area of a rhombus?
4.Can a rhombus have right angles?
Common Mistakes and How to Avoid Them in Properties of Rhombuses
Students tend to get confused when understanding the properties of a rhombus, and they tend to make mistakes while solving problems related to these properties. Here are some common mistakes students tend to make and the solutions to these common mistakes.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
