109 LearnersLast updated on August 13th, 2025
Properties of Isosceles Trapezium
An isosceles trapezium is a type of quadrilateral with unique properties. These properties help students simplify geometric problems related to isosceles trapeziums. The properties of an isosceles trapezium include having one pair of parallel sides, and the non-parallel sides (legs) are equal in length. Additionally, the base angles 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 an isosceles trapezium.
What are the Properties of an Isosceles Trapezium?
The properties of an isosceles trapezium 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 an isosceles trapezium, and some of them are mentioned below: Property 1: One pair of parallel sides An isosceles trapezium has one pair of parallel sides, known as the bases. Property 2: Equal non-parallel sides The non-parallel sides (legs) are equal in length. Property 3: Equal base angles The base angles of an isosceles trapezium are equal. Property 4: Symmetry The isosceles trapezium has one line of symmetry perpendicular to the parallel sides. Property 5: Area Formula The formula used to calculate the area of an isosceles trapezium is given below: Area = ½ x (base1 + base2) x height Here, base1 and base2 are the lengths of the parallel sides, and height is the perpendicular distance between them.
Tips and Tricks for Properties of an Isosceles Trapezium
Students often confuse and make mistakes while learning the properties of an isosceles trapezium. To avoid such confusion, we can follow the following tips and tricks: One Pair of Parallel Sides: Students should remember that an isosceles trapezium has only one pair of parallel sides, which are its bases. Equal Non-Parallel Sides: Students should remember that the non-parallel sides (legs) of an isosceles trapezium are always equal in length. Equal Base Angles: Students should remember that the base angles on each side of an isosceles trapezium are equal.
Confusing an Isosceles Trapezium with a Regular Trapezium
Students should remember that an isosceles trapezium has equal non-parallel sides, unlike a regular trapezium.
Mistake 1
Misinterpreting Angle Relationships
Students should know and remember that the base angles of an isosceles trapezium are equal.
Mistake 2
Incorrectly Applying the Area Formula
Students should practice the formula used to find the area of an isosceles trapezium, which is given below. The students must also understand the representations of base1, base2, and height. Area = ½ x (base1 + base2) x height
Mistake 3
Forgetting the Equal Leg Rule
Students must remember that an isosceles trapezium has non-parallel sides (legs) that are equal in length.
Mistake 4
Solved Examples on the Properties of Isosceles Trapeziums
In an isosceles trapezium, the bases are marked as AB and CD, where AB = 6 cm and CD = 10 cm. If the non-parallel sides (legs) are equal, what is the length of side AD?
AD = 5 cm.
Problem 1
In an isosceles trapezium, the non-parallel sides (legs) are equal. Since AD and BC are equal and AB is 6 cm while CD is 10 cm, if AD = 5 cm, then BC = 5 cm as well.
In an isosceles trapezium ABCD, angle ABC = 75 degrees. What is the measure of angle DAB?
Explanation
DAB = 75 degrees.
Problem 2
In an isosceles trapezium, the base angles are equal. Here, angles ABC and DAB are base angles. Hence, angle DAB = 75 degrees.
The diagonals of an isosceles trapezium intersect at point O. If angle AOB is not given, what can you conclude about the diagonals?
Explanation
Diagonals of an isosceles trapezium are not necessarily perpendicular.
Problem 3
Although the diagonals intersect, they do not have to intersect at right angles in an isosceles trapezium, unlike a kite.
In isosceles trapezium ABCD, if the height from A to base CD is 4 cm and CD = 10 cm, AB = 6 cm, what is the area of the trapezium?
Explanation
Area = 32 sq cm.
Problem 4
Using the area formula, area = ½ x (base1 + base2) x height Substituting the values, we get Area = ½ x (6 + 10) x 4 = 32 cm².
An isosceles trapezium has bases of length 8 cm and 12 cm. If the height is 5 cm, what is the area of the trapezium?
Explanation
Area = 50 sq cm.
An isosceles trapezium is a quadrilateral with one pair of parallel sides and equal non-parallel sides (legs).
1.How many pairs of equal sides does an isosceles trapezium have?
2.Are the diagonals of an isosceles trapezium equal?
3.How do you find the area of an isosceles trapezium?
4.Can an isosceles trapezium have all four sides equal?
Common Mistakes and How to Avoid Them in Properties of Isosceles Trapeziums
Students tend to get confused when understanding the properties of an isosceles trapezium, 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.
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.
