Classification of Triangles

Since there are two main elements in any triangle, that are its sides and angles.

So, triangles are classified, or grouped, in two different ways.

  a) On the basis of sides

  b) On the basis of angles

Classification of triangles on the basis of sides

Scalene Triangle

A triangle in which all three sides are of different length (non-congruent) is called a scalene triangle.

Isosceles Triangle

A triangle in which two of its sides are equal in length (i.e. two sides are congruent) is called an isosceles triangle. (The slash marks indicate equal measure.)

Equilateral Triangle

A triangle which has all its three sides are of equal length (i.e. all sides are congruent) is called an equilateral triangle. (The slash marks indicate equal measure.)

Classification of triangles on the basis of angles  

Acute Angled Triangle

A triangle whose all three angles are acute, that is less than 90° is called an acute angled triangle or acute triangle.

Obtuse Angled Triangle

A triangle whose one angle is obtuse, that is more than 90° but less than 180° is called an obtuse angled or obtuse triangle.

Right Angled Triangle

A triangle whose one angle is a right angle (that is 90°) is called a right angled triangle or right triangle.

Equiangular Triangle

A triangle which has all its three angles are of equal measurement i.e. 60° is called an equiangular triangle.

The sides of an equiangular triangle are all the same length (congruent), and so an equiangular triangle is really the same thing as an equilateral triangle.

Properties of Triangles

Property 1: The sum of three angles of a triangle equals to 180°. So, if two angles of a triangle are given, we can easily find out its third angle.

Example: In a right angled triangle, if one angle is 70°, find its third angle.

Solution: Triangle is a right triangle that is one angle is right angle.

Given, first angle = 90°; second angle = 70°

Therefore third angle = 180° – (angle I + angle II)

= 180° – (90° + 70°) = 180° – 160°

Third angle = 20°

Property 2: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. This mean if we add any two side of the triangle, the sum is more than its third side.

Example: Is it possible to have a triangle whose sides are 6cm, 7cm and 8cm respectively?

Solution: The lengths of the sides are 6cm, 7cm and 8cm respectively.

a)   6cm + 7cm > 8cm

b)   7cm + 8cm > 6cm

c)   8cm + 6cm > 7cm

Hence, a triangle with these sides is possible.

Example: Is the construction of a triangle possible in which the lengths of sides are 6cm, 7cm and 13cm respectively?

Solution: The lengths of sides are 6cm, 7cm and 13cm.

6cm + 7cm = 13cm

Here, the sum of two smaller sides is equal to the third side. But in a triangle, the sum of any two sides should be greater than third side.

Hence, no triangle is possible with sides 6cm, 7cm and 13cm

Some More Facts About A Triangle

1. If all the three sides of a triangle are equal, then all its three angles are also equal. This mean an equilateral triangle is also an equiangular triangle.

2. In an isosceles triangle, the angles opposite to the equal sides are equal.

3. An acute angled triangle may be scalene, isosceles or equilateral.

4. In an obtuse angled triangle, the side opposite to the obtuse angle is the longest