Math is always fun learning. It will be very interesting when solving the problems in different ways. We have provided the information on each and every topic in 5th Grade Math here. So, we suggest the students make use of our page to understand the concepts in depth. Here on this page, we are going to learn about the classification of triangles. Before knowing about the classification of triangles, the students must know about the triangle. So, let us see the triangle types and then focus on classification or types of triangles. Here you can find examples of the classification of triangles with step by step explanation.

## What is a Triangle?

A triangle is a two-dimensional closed figure with three sides and three angles. Each segment is called a side and the point where two sides meet is known as the vertex.

### Classification of Triangle Definition

There are six types of triangles with respect to the length and measure of lines and angles of triangles. A triangle is a specific type of polygon that has three sides and three angles. The triangles are classified into two ways.They are given as follows,

i. Triangles based on the lengths of their sides

ii. Triangles based on their interior angles.

**Based on their sides:**

1. Scalene Triangle

2. Isosceles Triangle

3. Equilateral Triangle

**Based on their Angles:**

4. Acute Triangle

5. Obtuse Triangle

6. Right Triangle

### How do we Classify a Triangle?

Triangles can be classified by side length and angles. Each of them is explained with necessary diagrams and definitions in the further modules. They are as under

#### Types of Triangle Based on Sides

###### 1. Scalene Triangle

A scalene triangle has three different sides. None of the sides are equal in the scalene triangle. In a scalene triangle, all the interior angles are different. The scalene triangle does not have any congruent sides.

###### 2. Isosceles Triangle

A triangle with two equal sides is called the Isosceles triangle. An Isosceles triangle has two congruent sides. So, the angles opposite the equal sides are equal to each other. In other words, an isosceles triangle has two equal sides and two equal angles.

###### 3. Equilateral Triangle

In an equilateral triangle, all sides are equal. All the angles of an equilateral triangle are equal as well measuring 60 degrees.

#### Types of Triangle Based on Angles

###### 4. Acute Triangle

An acute angle is a triangle whose all three interior angles are acute. If all the interior angles are less than 90 degrees then it is an acute-angled triangle.

###### 5. Obtuse Triangle

Obtuse angle triangles are those in which one of the three interior angles has more than 90 degrees. If one of the angles in the triangle has greater than 90 degrees then that triangle is said to be an obtuse triangle.

###### 6. Right Triangle

A triangle in which one of the angles is 90 degrees is called right-angled triangle. In a right angle triangle, the side opposite to the right angle will be the longest side which is called the hypotenuse.

### Triangle and its Classification Examples

**Example 1.**

Fill in the blanks

1. A triangle with all sides are equal is called …………

2. A triangle with two sides are equal is called …………

3. If none of the sides are equal then that triangle is known as …….

**Solution:**

1. A triangle with all sides are equal is called **Equilateral Triangle.**

2. A triangle with two sides that are equal is called **Isosceles Triangle.**

3. If none of the sides are equal then that triangle is known as **Scalene Triangle.**

**Example 2.**

Classify the triangle with the sides 5 cm, 6 cm, and 6 cm.

**Solution:**

A triangle with two sides that are equal is called Isosceles Triangle.

The name of the triangle based on sides is 5 cm, 6 cm, and 6 cm.

So, the classification of the triangle is Isosceles.

**Example 3.**

Classify the triangle with the sides 8 cm, 8 cm, and 8 cm.

**Solution:**

A triangle with all sides are equal is called Equilateral Triangle.

The sides are 8 cm, 8 cm, and 8 cm.

We observe that all the sides are equal.

So, the classification of the triangle is Equilateral.

**Example 4.**

Classify the triangle with the angles 90°, 60°, and 30°.

**Solution:**

Given the angles 90°, 60°, and 30°.

One among the three angles is 90 degrees, thus it is a right triangle.

**Example 5.**

Classify the triangle with the angles 60°, 60°, and 60°.

**Solution:**

Given, the angles 60°, 60°, and 60°.

Each of the interior angles will have a measure of 60 degrees.

Thus the classification of the triangle based on the angle is an equilateral and acute triangle.

### Frequently Asked Questions on Classification of Triangles

**1. What are the classification of triangles?**

There are two ways of classification of triangles

1. based on sides (Scalene Triangle, Isosceles Triangle, Equilateral Triangle)

2. based on angles (Acute Triangle, Right Triangle, Obtuse Triangle).

**2. What are 3 ways to classify a triangle by its sides?**

The 3 ways to classify a triangle by its sides are given below.

Scalene triangle: a triangle with no congruent sides.

Isosceles triangle: a triangle with at least 2 congruent sides.

Equilateral triangle: a triangle with exactly 3 congruent sides.

**3. What are the 4 types of triangles?**

Triangle Types and Classifications: Isosceles, Equilateral, Obtuse, Acute, and Scalene.