Triangle

As the name suggests, the triangle is a polygon that has three angles. So, when does a closed figure has three angles.

When it has three line segments joined end to end.

Thus, we can say that a triangle is a polygon, which has three sides, three angles, three vertices and the sum of all three angles of any triangle equals 180⁰.

Properties of a triangle

These are the properties of a triangle:

• A triangle has three sides, three angles, and three vertices.
• The sum of all internal angles of a triangle is always equal to 180^0. This is called the angle sum property of a triangle.
• The sum of the length of any two sides of a triangle is greater than the length of the third side.
• The side opposite to the largest angle of a triangle is the largest side.
• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Types of triangles

Triangles can be classified in 2 major ways:

• Classification according to internal angles
• Classification according to the length of its sides

Types of Triangles Based on Sides

According to the lengths of their sides, triangles can be classified into three types which are:

1. Scalene
2. Isosceles
3. Equilateral

Scalene Triangle

A scalene triangle has all side lengths of different measures. No side will be equal in length to any of the other sides in such a triangle. In a scalene triangle, all the interior angles are also different. The figure given below illustrates a scalene triangle. You can see how none of the sides is equal in length.

In the above-given figure, you can see that all the sides of the triangle seem to be unequal.

Perimeter of a Triangle

The perimeter of a triangle is the distance covered around the triangle and is calculated by adding all the three sides of a triangle.

• The perimeter of a triangle = P = (a + b + c) units

where a, b and c are the sides of the triangle.

(Heron’s Formula)

The area of a triangle with 3 sides of different measures can be found using Heron’s formula. Heron’s formula includes two important steps. The first step is to find the semi perimeter of a triangle by adding all the three sides of a triangle and dividing it by 2. The next step is that, apply the semi-perimeter of triangle value in the main formula called “Heron’s Formula” to find the area of a triangle.

where, s is semi-perimeter of the triangle = s = (a+b+c) / 2

Isosceles Triangle

In an isosceles triangle, the lengths of two of the three sides are equal. 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.  The figure given below illustrates an isosceles triangle.