In Mathematics, there are a plethora of shapes and sizes, and Triangles are known to be one of the most important shapes. Triangles in real life can be seen in so many things, for instance, Traffic signals, Front and back views of the pyramids, the Bermuda Triangle, etc. Triangles are really significant as it has a base for support and can be used in building bases and trusses. There are various types of triangles. All these types and their properties are given in this article.

What is Triangle?

Triangles are three-sided closed polygons formed by the intersection of three lines. It is encountered a lot in everyday life. It is one of the basic shapes of geometry. It has three sides, three angles, and three vertices. The figure below shows a triangle ABC with vertices and angles A, B, and C. The sides of this triangle are AB, AC, and BC.

What are the Different Types of Triangles?

There are various types of classification on the basis of which Triangles are classified. Most important are on the basis of Sides and on the basis of angles.

Types of Triangles on the basis of Sides

On the basis of sides, There are 3 types of triangles

  • Equilateral Triangle
  • Isosceles Triangle
  • Scalene Triangle

Let’s discuss these types in detail.

Equilateral Triangles

Triangles having all sides and all angles equal are known as equilateral triangles. Since all the angles are equal, each angle is equal to 60° and the other name of an equilateral triangle is the Equiangular triangle.

Isosceles Triangles

The triangles have two sides equal and the third one is not equal to the rest two is called the isosceles triangle. The angles opposite to the equal sides of the triangle are also equal.

Scalene Triangles

A Scalene triangle is one which has none of its sides equal to each other and also, none of the angles are equal to each other, but the general properties of the triangle are applied to the scalene triangle as well. Hence, the sum of all the interior angles is always equal to 180°

Classification of Triangles

Triangles are the most fundamental shape in geometry and can be classified based on two things:

  • Interiors Angles
  • Sides of Triangles

Let’s understand these different classifications in detail.

Types of Triangles on the Basis of Sides

There are three types of triangles based on the lengths of sides and their equality with each other, that are as follows:

  • Equilateral Triangle
  • Isosceles Triangle
  • Scalene Triangle

As we already discuss these in the article we won’t be discussing these topics again.

Types of Triangles on the Basis of Angles

Based on the interior angles of a triangle, we can classify the triangle into three types:

  • Acute Angled Triangle
  • Right Angled Triangle
  • Obtuse Angles Triangle

Let’s discuss these types in detail.

Acute Angled Triangle

An Acute angled Triangle is one where all the interior angles of the Triangle are less than 90°. For Instance, an Equilateral Triangle is an acute-angled triangle (all angles are less than 90°).

Right Angled Triangle

A Right Angled Triangle is one where one of the angles is always equal to 90°. Pythagoras’ Theorem is derived for Right angled triangles, Which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the base and perpendicular.

Obtuse Angled Triangle

An obtuse angled triangle has one of the sides more than 90°, In this case, since one of the three angles is more than 90°, the rest of the two angles is less than 90°.

Obtuse Angled Triangle

Classification Based on the Sides and Angles of Triangle

There are various other types of triangles based on both angles and sides of the triangle, some of these types are:

  • Isosceles Right Triangle
  • Obtuse Isosceles Triangle
  • Acute Isosceles Triangle
  • Right Scalene Triangle
  • Obtuse Scalene Triangle
  • Acute Scalene Triangle

Let’s discuss these types of triangles in detail.

Isosceles Right Triangle

A Triangle with two equal sides and one right angle is called Isosceles Right Triangle or Isosceles Right Angle Triangle. For example, a triangle ABC with sides AB = BC = 8 cm, and ∠B = 90°, is an example of an Isosceles Right Angle Triangle.

Obtuse Isosceles Triangle

An Isosceles triangle (triangle with two sides equal) with one obtuse angle (angle greater than 90°) is called Obtuse Isosceles Triangle. For example, a triangle PQR with sides PQ = PR = 10 cm and ∠P = 110°, is an example of an Obtuse Isosceles Triangle.

Acute Isosceles Triangle

A triangle with two sides equal (Isosceles triangle) with each other and all the interior angles less than the right angle, is called Acute Isosceles Triangle. For example, a triangle LMN with sides LM = LN = 8 cm and ∠M = ∠N = 70°, is an example of an Acute Isosceles Triangle.

Examples of Isosceles Triangles

Right Scalene Triangle

A Right triangle with all sides of different lengths is called Right Scalene Triangle. For example, a triangle ABC with sides AC = 6 cm, BC = 8 cm, AB = 10 cm, and ∠C = 90°, is an example of a Right Scalene Triangle.

Obtuse Scalene Triangle

A Triangle with all sides of different lengths, as well as one obtuse angle, is called Obtuse Scalene Triangle. For example, a triangle DEF with sides DE = 9 cm, EF = 7 cm, DF = 5 cm, and ∠F = 135°, is an example of an Obtuse Scalene Triangle.

Acute Scalene Triangle

A Triangle with all angles less than the right angle and all different side lengths is called Acute Scalene Triangle. For example, a triangle GHI with sides GH = 5 cm, HI = 7 cm, IG = 9 cm, and ∠I = 60°, is an example of an Acute Scalene Triangle.

Examples of Scalene Triangles

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FAQs on Types of Triangles

1. Define Triangle.

A triangle is a two-dimensional geometric shape that is formed by connecting three vertices with three line segments while making three interior angles as well.

2. What are Different Basis on which Triangles can be Classified?

There are various types of triangles based on different parameters of classification i.e.,

  • Based on Sides
  • Based on Interior Angles

3. How are Triangles Classified Based on Sides?

Based on the sides, triangles can be classified as follows:

  • Equilateral Triangle
  • Isosceles Triangle
  • Scalene Triangle

4. What are Different Types of Triangles Based on Angles?

Based on the measurement of interior angles, triangles can be classified as follows:

  • Acute Angle Triangle
  • Right Angle Triangle
  • Obtuse Angle Triangle

5. Are there any Triangles that have both Equal sides and Equal angles?

Yes, there is a triangle where each angle and side is equal i.e., equilateral triangle.

6. Are there any Triangles that do not fit into any of the classifications?

No, there is no such triangle which we can’t fit under any classification

7. Can a Triangle be both Obtuse and Isosceles?

Yes, a triangle can be both obtuse as well as isoceles and is called Obtuse Isosceles Triangle.

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