Properties of Isosceles Trapezium
2026-02-28 17:58 Diff
https://brightchamps.com/en-us/math/geometry/properties-of-isosceles-trapezium

239 Learners

Last updated on August 13, 2025

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.

Explore Our Programs

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.

Okay, lets begin

In an isosceles trapezium ABCD, angle ABC = 75 degrees. What is the measure of angle DAB?

Explanation

DAB = 75 degrees.

Well explained 👍

Problem 2

In an isosceles trapezium, the base angles are equal. Here, angles ABC and DAB are base angles. Hence, angle DAB = 75 degrees.

Okay, lets begin

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.

Well explained 👍

Problem 3

Although the diagonals intersect, they do not have to intersect at right angles in an isosceles trapezium, unlike a kite.

Okay, lets begin

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.

Well explained 👍

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.

Okay, lets begin

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.

Well explained 👍

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?

An isosceles trapezium has one pair of equal non-parallel sides (legs).

2.Are the diagonals of an isosceles trapezium equal?

Yes, the diagonals of an isosceles trapezium are equal in length.

3.How do you find the area of an isosceles trapezium?

To find the area of an isosceles trapezium, students must apply the formula: ½ x (base1 + base2) x height.

4.Can an isosceles trapezium have all four sides equal?

No, an isosceles trapezium has only two equal non-parallel sides. If all sides are equal, it would be a rhombus.

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.

What Is Geometry? 📐 | Shapes, Angles & 🎯 Fun Learning for Kids | ✨BrightCHAMPS Math

▶

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.