# Isosceles Triangle Definition

It is one of three major types of triangles divided on the basis of their lengths. An Isosceles Triangle is one in which any** two sides or arms** are of **equal lengths** with **equal** corresponding **angles**.

Triangle is a specific term of **Geometry** that represents shapes with **three sides** and **three angles**. There are three major types of triangles used in Mathematics. All of those are distinguished mainly based on their **side’s length**.

**Note:**

You can read about Triangle here.

**Table of Contents**

## Real-life examples of Isosceles Triangle

There are different parts of daily routine equipment that make an isosceles triangle. Let us show you a few examples of them to have a better idea.

- The base of a clothing hanger
- The base of the guitar connected with its strings
- Traffic controlling sign boards.

Amazing to know? You can also explore this type of triangle in many other products in your surroundings by using your creative thoughts.

### Parts of an Isosceles Triangle

Like other shapes in **Geometry**, the Isosceles triangle also has three major parts. Let us show you briefly about those parts here.

**Note:**

Read about Axis in Geometry here.

**Legs**: The equal sides of an Isosceles triangle are collectively called the Legs of that particular Triangle.**Base**: The third side of an Isosceles triangle is called the Base of the triangle. It can be larger or shorter than the legs of the triangle.**Vertex Point**: It is a particular point of a triangle where both legs meet or join.

**Note:**

You can read about **Vertex** in detail here.

### Types of Isosceles Triangle

No doubt, the Isosceles triangle is different from other major types depending on the length of the sides. But it also has **three types** further depending on the angles of the triangle.

**Isosceles Acute Triangle**: An Isosceles triangle having all three angles less than 90 degrees is called Acute Isosceles Triangle.**Isosceles Right Triangle**: An Isosceles triangle having at least one angle of 90 degrees is called Right Isosceles Triangle.**Isosceles Obtuse Triangle**: An Isosceles triangle with at least one angle greater than 90 degrees is called Obtuse Isosceles Triangle.

### Basic operations on Triangles

As we all know that there are **two major** operations that can be performed on triangles i.e. **Area calculation and Perimeter calculation**. Let us show you how to find both of these for an Isosceles triangle

### How to find the Area of an Isosceles Triangle?

To find the Area of the Isosceles Triangle, we have a specific formula. It is given below:

Area of an Isosceles Triangle = 1/2 (Base × Height)

**Example 1:**

Find the Area of an Isosceles Triangle with following measurements.

Height = 3 cm

Base = 12 cm

**Solution:**

To find the Area, we only have to put these values in the above formula.

Area = 1/2 (12 × 3)

Area = 1/2 (36)

Area = 18 square cm

### How to find the Perimeter of an Isosceles Triangle?

Like Area, Isosceles triangle also has a specific formula to find the Perimeter. The formula is given below.

Perimeter of an Isosceles triangle = 2a + Base(b)

- Here
**“a”**represents the equal sides of the triangle.

**Example 2:**

Find the Parameter of the triangle with the following measurements.

a = 12 cm

b = 32 cm

**Solution:**

To find the Perimeter of an Isosceles triangle, we need to put the values in the above formula.

Perimeter = 2 (12) + 32

Perimeter = 24 + 32

Perimeter = 56 cm

### Fun Facts about Isosceles Triangle

- The sum of angles of an Isosceles triangle is 180 degrees. e.
- The angles correspond to sides with equal lengths are also equal to each other.
- An Isosceles right triangle has at least one angle of 90 degrees.
- A right Isosceles triangle has two angles of 45 degrees.

### Other Types of Triangles

Along with the Isosceles triangle, there are two other types. Let us tell you about them here briefly.

**Note:**

Read about **Scalene Triangle** here.

**Scalene Triangle:**It is a type of triangle having all**three sides with different lengths**. Such a triangle has all three angles of different measurements.**Equilateral Triangle**:This type of triangle has**all three sides of equal measurement**. The angles in this triangle must be equal to each other.

**Note:**

Read about Area of an Equilateral Triangle here.

### FAQ's

**How to know if a triangle Isosceles or not?**

If a triangle has two sides with equal lengths and two angles of equal measurement, it is said to be an Isosceles triangle.

**What is the sum of angles in an Isosceles Triangle?**

The sum of the angles of all triangles is 180 degrees.

**Does an Isosceles Triangle have equal angles? **

Yes, the sides with the same angles must have angles with the same measurements.

**What are the three major types of the Isosceles Triangle?**

An isosceles triangle has three major types mentioned below.

- Acute Isosceles Triangle
- Right Isosceles Triangle
- Obtuse Isosceles Triangle