Classification of Triangle on the Basis of its Various Properties

A triangle is a two-dimensional geometrical figure that we can encounter in our daily lives. Various examples of triangles that we can see in real-life are pizza slices, nachos, traffic signs, and so on. This geometrical figure has three sides, three angles, and three vertices.

There are different types of triangle, each classified on the basis of its sides, angles, or some other property. In this article, we will discuss in detail the various types of triangles classified on the basis of sides or angles, but before that let us discuss an interesting type of triangle discovered by the great French mathematician, Blaise Pascal.

Different Types of Triangles

Classification on the Basis of Sides of the Triangle

Triangles can be classified into three different categories based on the length of their sides which are as follows:

Scalene Triangle: A scalene triangle can be classified as the one in which none of the sides of the triangle are equivalent to each other.
Isosceles Triangle: An isosceles triangle can be classified as the one in which two sides of the triangle are equivalent or congruent to each other.
Equilateral Triangle: An equilateral triangle can be classified as the one in which all the sides of the triangle are equivalent to each other.

Classification on the Basis of Angles of the Triangle

Triangles can be classified into three different categories based on their angles which are as follows:

Acute Triangle: An acute triangle can be classified as the one in which all the angles of the triangle are acute, which means that they are less than 90 degrees. It is sometimes also known as the acute-angled triangle.
Right Triangle: A right triangle can be classified as the one in which one of the angles of the triangle measures 90 degrees. The other two angles of the right triangle are always acute, which means that they are less than 90 degrees. It is sometimes also known as the right-angled triangle.
Obtuse Triangle: An obtuse triangle can be classified as the one in which one of the angles of the triangle measures more than 90 degrees. The remaining two angles are always acute. It is sometimes also known as the obtuse-angled triangle.

What Do You Mean by Pascal’s Triangle?

When binomial coefficients are arranged in a triangular form, it forms a triangle known as Pascal’s Triangle, named after the great Mathematician, Blaise Pascal. We use Pascal’s triangle in important concepts like probability, algebra, and combinatorics.

In Pascal’s triangle, the different numbers are placed one above the other in such a way that each number is the sum of the two numbers. We use this special type of triangle generally to find out the probability of heads or tails in the tossing of a coin, to find out the coefficients of binomial expansion, and in combinations of certain things.

Some Important Points To be Noted

While studying about triangles and their types, we must keep in mind the following points:

The summation of all the three internal angles of any triangle is 180 degrees.
All the types of triangles will have at least two angles that are acute, which means that they will be less than 90 degrees.
In an equilateral triangle, all the internal angles measure the same i.e. 60 degrees.
If all the angles and the sides of any given triangle measure the same, it is known as the equiangular triangle or the equilateral triangle.

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