104 LearnersLast updated on August 6th, 2025
Properties of Parallelogram
A parallelogram is a type of quadrilateral that has several distinctive properties. These properties help students simplify geometric problems related to parallelograms. The properties of a parallelogram include having opposite sides that are equal in length and parallel, and opposite angles that are equal. These properties help students analyze and solve problems related to symmetry, angles, and area. Now let us learn more about the properties of a parallelogram.
What are the Properties of a Parallelogram?
The properties of a parallelogram are straightforward, aiding students in understanding and working with this type of quadrilateral. These properties are derived from the principles of geometry. There are several properties of a parallelogram, and some of them are mentioned below: Property 1: Opposite sides are equal and parallel In a parallelogram, both pairs of opposite sides are equal in length and parallel to each other. Property 2: Opposite angles are equal The angles opposite each other in a parallelogram are equal. Property 3: Diagonals The diagonals of a parallelogram bisect each other. Property 4: Consecutive angles are supplementary The consecutive angles in a parallelogram add up to 180 degrees. Property 5: Area Formula The formula used to calculate the area of a parallelogram is given below: Area = base x height
Tips and Tricks for Properties of a Parallelogram
Students often confuse and make mistakes while learning the properties of a parallelogram. To avoid such confusion, we can follow the following tips and tricks: Opposite Sides are Equal and Parallel: Students should remember that in a parallelogram, both pairs of opposite sides are equal in length and parallel. To verify this, students can draw a parallelogram and observe that the opposite sides are equal in length and parallel. Diagonals Bisect Each Other: Students should remember that in a parallelogram, the diagonals bisect each other. Consecutive Angles are Supplementary: Students should remember that in a parallelogram, any two consecutive angles add up to 180 degrees.
Confusing a Parallelogram with a Rectangle
Students should remember that a parallelogram has equal and parallel opposite sides, while a rectangle has all angles equal to 90 degrees.
Mistake 1
Misinterpreting the Diagonal Relationship
Students should know and remember that the diagonals of a parallelogram bisect each other, but they are not necessarily equal unless it is a rectangle or rhombus.
Mistake 2
Incorrectly Applying the Formula
Students should practice the formula used to find the area of a parallelogram, which is given below. The students must also understand that the base and height must be perpendicular to each other. Area = base x height
Mistake 3
Misunderstanding Angle Relationships
Students should remember that opposite angles in a parallelogram are equal, and consecutive angles are supplementary, meaning they add up to 180 degrees.
Mistake 4
Forgetting the Parallel Side Rule
Students must remember that in a parallelogram, opposite sides are both equal in length and parallel.
Mistake 5
Solved Examples on the Properties of Parallelograms
In a parallelogram, the four corners are marked as A, B, C, and D. If AB = 6 cm, BC = 8 cm, and CD = 6 cm, what is the length of the side DA?
DA = 8 cm.
Problem 1
In a parallelogram, opposite sides are equal. Since AB = 6 cm and CD = 6 cm, then BC = DA. Hence, DA = 8 cm.
In a parallelogram ABCD, the angle ABC = 120 degrees. What is the measure of angle ADC?
Explanation
ADC = 60 degrees
Problem 2
In a parallelogram, consecutive angles are supplementary, meaning they add up to 180 degrees. Here, angle ABC and angle ADC are consecutive. Hence, angle ADC = 180 - 120 = 60 degrees.
The diagonals of a parallelogram intersect at point O. If angle AOB = 75 degrees, what can you conclude about the diagonals of the parallelogram?
Explanation
Diagonals of the parallelogram bisect each other.
Problem 3
According to a property of parallelograms, the diagonals bisect each other.
In parallelogram ABCD, diagonal AC bisects diagonal BD at a point E. If BE = 5 cm, what is the length of ED?
Explanation
ED = 5 cm
Problem 4
Since BE = 5 cm and the diagonals bisect each other, ED = BE = 5 cm.
A parallelogram has a base of 12 cm and a height of 5 cm. What is the area of the parallelogram?
Explanation
Area = 60 sq cm.
A parallelogram is a quadrilateral where both pairs of opposite sides are equal in length and parallel.
1.How many pairs of equal sides does a parallelogram have?
2.Are all angles in a parallelogram equal?
3.How do you find the area of a parallelogram?
4.Can a parallelogram have all sides equal?
Common Mistakes and How to Avoid Them in Properties of Parallelograms
Students tend to get confused when understanding the properties of a parallelogram, and they tend to make mistakes while solving problems related to these properties. Here are some common mistakes students tend to make and solutions to these common mistakes.
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.
