Triangles are a fundamental geometric shape in mathematics, consisting of three sides and three angles. There are several types of triangles, classified based on their sides and angles. The most common classifications are:

  1. By Sides:- 

       a) Isosceles Triangle:- Two sides are of equal length, and the third is different.

       b) Scalene Triangle:- All three sides are of different lengths.

       c) Equilateral Triangle:- All three sides are of equal length. 

   2. By Angles:-

        a) Acute Triangle:- All three angles are less than 90 degrees.

        b) Right Triangle:- One angle is exactly 90 degrees.

        c) Obtuse Triangle:- One angle is greater than 90 degrees.


Triangles have various properties and theorems associated with them, such as the Pythagorean Theorem, which applies to right-angled triangles and states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The sum of the interior angles of any triangle is always 180 degrees. This property is known as the Triangle Sum Theorem. Triangles are also the building blocks for more complex shapes and are widely used in geometry and trigonometry.