106 LearnersLast updated on August 6th, 2025
Properties of Rhombus
A rhombus is a type of quadrilateral that has many interesting properties. Understanding these properties helps students simplify geometric problems related to rhombuses. The properties of a rhombus include having all sides equal in length and diagonals that bisect each other at right angles. These properties assist students in analyzing and solving 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 straightforward and help students 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: All Sides are Equal A rhombus has four sides that are equal in length. Property 2: Opposite Angles are Equal The opposite angles of a rhombus are equal. Property 3: Diagonals The diagonals of a rhombus bisect each other at right angles. Each diagonal divides the rhombus into two congruent triangles. 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 x d1 x d2 Here, the lengths of the diagonals are represented as d1 and d2.
Tips and Tricks for Properties of a Rhombus
Students may confuse properties of the rhombus with those of other quadrilaterals. To avoid such confusion, we can follow the following tips and tricks: All Sides are Equal: Students should remember that in a rhombus, all four sides are equal in length. To verify this, students can draw a rhombus and measure the sides to confirm they are equal. Diagonals are Perpendicular: Students should remember that in a rhombus, the diagonals always intersect at right angles. Diagonals Bisect Each Other: Students should remember that in a rhombus, each diagonal bisects the other into two equal parts.
Confusing a Rhombus with a Square
Students should remember that while all sides of a rhombus are equal, the angles are not necessarily 90 degrees, which distinguishes a rhombus from a square.
Mistake 1
Misinterpreting the Diagonal Relationship
Students should know and remember that the diagonals of a rhombus bisect each other at right angles and divide the rhombus into four congruent right triangles.
Mistake 2
Incorrectly Applying the Formula
Students should practice the formula used to find the area of a rhombus, given below. They must also understand the representations of d1 and d2. Area = ½ x d1 x d2
Mistake 3
Misunderstanding Angle Relationships
Students should remember that in a rhombus, opposite angles are equal, and the adjacent angles are supplementary (add up to 180 degrees).
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 = 5cm, what are the lengths of sides BC, CD, and DA?
BC = 5cm, CD = 5cm, DA = 5cm.
Problem 1
In a rhombus, all four sides are equal in length. Since AB = 5cm, then BC = CD = DA = 5cm.
In a rhombus ABCD, angle ABC = 120 degrees. What is the measure of angle ADC?
Explanation
ADC = 120 degrees
Problem 2
In a rhombus, 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 a point E. If BE = 4cm, what is the length of ED?
Explanation
ED = 4cm
Problem 4
Since BE = 4cm and the diagonals bisect each other, ED = BE = 4cm.
A rhombus has diagonals of length 12cm and 16cm. What is the area of the rhombus?
Explanation
Area = 96 sq cm.
A rhombus is a quadrilateral with all four sides equal in length.
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 can get confused when understanding the properties of a rhombus and may make mistakes while solving problems related to these properties. Here are some common mistakes students tend to make and solutions to avoid them.
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.
