# Classification of Triangles – Definition, Types, Examples

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## What Is the Classification of Triangles?

The classification of triangles can be done easily based on the measurement of sides and angles. Triangles are classified on the basis of

• the length of three sides
• the measurement of three angles
• the measurement of sides and angles

A triangle has three sides, interior angles, and vertices. There are different names for triangles depending on the type of classification. These names have the keywords that express the nature and properties of the triangle.

Take a look at the table below to understand triangle classification.

## Classification of Triangles Based on Sides

We can begin classifying triangles based on the sides of the shape. Every triangle has three sides, but the length of these sides determines the type of triangle. Sometimes, the ratio of the lengths of the sides of the triangle may be more relevant to classify a triangle rather than its sole unit measure. Three types of triangles emerge in this scenario. We classify the triangles by its sides as equilateral, isosceles, and scalene.

### Equilateral Triangle

It is a regular polygon, and as the name suggests, it has equal sides and angles. Each side of such a triangle is equal, and so are its angles, at 60 degrees.

### Isosceles Triangle

An isosceles triangle is one that has two equal sides. These sides are known as the legs of the triangle, and the angle formed between them is called the vertex angle.

### Scalene Triangle

A scalene triangle is one in which all sides and angles are different.

## Classification of Triangles Based on Angles

Another way in which we can perform the classification of triangles is on the basis of angles. As is apparent, every triangle has three angles. The sum of the measures of these angles is a total of 180 degrees.

Take a look at the image showing the triangle classification by angles.

### Acute Triangle

An acute triangle is formed when all three interior angles of a triangle measure less than 90 degrees. Its sides may or may not be equal.

### Right Triangle

A right triangle is one in which at least one of the angles is 90 degrees. This angle is called a right angle. According to the Pythagoras’ theorem, the side of the triangle opposite the right angle is the largest in the triangle. It is called the hypotenuse.

### Obtuse Triangle

Another type of triangle in geometry is obtuse types of triangles. In this case, one of the angles of the triangle is larger than 90 degrees. The sum of the other two angles in the triangle is less than 90 degrees.

## Classification of Triangles Based on Angles and Sides

Classification of triangles can be done on the basis of the sides and angles of the triangle. Following are the 6 different types of triangles based on this classification.

### Equiangular Triangle

An equiangular triangle is one in which all the sides and angles of the triangle are equal. It is also known as an equilateral triangle.

### Isosceles Right Triangle

In an isosceles right triangle, two sides of a triangle are equal, and any one angle of the triangle is equal to 90 degrees. The two other angles are congruent.

### Obtuse Isosceles Triangle

An obtuse isosceles triangle is one in which two sides of the triangle are equal, and one of the angles is obtuse.

### Acute Isosceles Triangle

In this type of triangle, all three angles of the triangle are acute, and any two sides of the triangle are equal.

### Right Scalene Triangle

A right scalene triangle is one in which any one of the angles is a right angle, but all the sides of the triangle are unequal.

### Obtuse Scalene Triangle

In this type of triangle, one of the angles is an obtuse angle, and all the sides of the triangle measure differently.

### Acute Scalene Triangle

This triangle has three unequal sides and three acute angles, which is why it is called an acute scalene triangle.

## Solved Examples On Classification of Triangles

1. If the length of all three sides of a triangle is not equal, identify the type of triangle according to the classification of triangles.

Solution: This type of triangle is a scalene triangle. In this type of triangle, the length of the three sides of the triangle is different from each other.

2. Based on the properties of a triangle, if the measure of the angle at the vertices of a triangle is 60 degrees, identify the type of triangle based on the classification of triangles.

Solution: A triangle with all angles measuring 60 degrees is an equilateral triangle. An equilateral triangle is one in which all the interior angles are the same, measuring 60 degrees each. In this case, the sum of all the angles of the triangle is 180 degrees.

3. If the lengths of a triangle are 4 in, 4 in, and 5 in, identify the type of the triangle.

Solution: This type of triangle is an isosceles triangle. An isosceles triangle is one in which two sides of a triangle are equal, and the third side of the triangle is different.

## Practice Problems On Classification of Triangles

1

### Based on the classification of triangles, which of the following combinations of angle measures will form an obtuse triangle?

$60^\circ,\;70^\circ,\;50^\circ$
$95^\circ,\;30^\circ,\;55^\circ$
$89^\circ,\;45^\circ,\;46^\circ$
$90^\circ,\;60^\circ,\;30^\circ$
CorrectIncorrect
Correct answer is: $95^\circ,\;30^\circ,\;55^\circ$
In an obtuse triangle, one of the vertex angles is an obtuse angle. Among the given options, only option B consists of an obtuse angle i.e. angle exceeding 90 degrees.
2

### If the angle of a triangle is 90 degrees, identify the type of the triangle from the options given below.

Isosceles triangle
Right-angled triangle
Equilateral triangle
Scalene triangle
CorrectIncorrect
A triangle with a right angle is called a right-angled triangle. It is defined on the basis of angles when performing the classification of triangles.
3

### Which of the following properties aptly describes a right-angled triangle?

Sides of the triangle are 4 cm, 4 cm, and 7 cm
Sides of the triangle are 5 cm, 10 cm, and 12 cm
Angles of the triangle are $60^\circ,\;60^\circ$ and $60^\circ$
Angles of the triangle are $90^\circ,\; 60^\circ$ and $30^\circ$
CorrectIncorrect
Correct answer is: Angles of the triangle are $90^\circ,\; 60^\circ$ and $30^\circ$
A right-angled triangle is classified by one angle in the triangle, which measures 90 degrees. Further, the sum of the other two angles of the triangle is not more than 90 degrees, which in this case is 60 and 30 degrees.

## Frequently Asked Questions On Classification of Triangles

Every equilateral triangle has three lines of symmetry. This is because each line of symmetry will always pass through a triangle’s vertex.

Every equilateral and isosceles triangle bears the properties of reflection symmetry. Reflection symmetry is a type of symmetry where one half of an object reflects the other half of the object. The name is also known as mirror symmetry.

Although equilateral and equiangular triangles are regular polygons, there lies a main difference between the two. An equilateral triangle usually has congruent sides, similar to a Rhombus but an equiangular triangle has congruent interior angles similar to a rectangle. If a polygon satisfies the condition of both equilateral and equiangular triangles, then it is considered a regular polygon.

Yes, an acute triangle can be a scalene triangle. We can always draw an acute triangle, whether it has equal sides. Only the angles of an acute triangle need to be less than 90 degrees to be called one such triangle.

Irrespective of the classification of triangles, the two conditions that all triangles must satisfy are

1. the sum of two sides of a triangle should be greater than the third side.
2. the sum of all the interior angles of the triangle must be 180 degrees.