Types of Triangles

Since all triangles have sides and angles, they can also be classified on the basis of these.

Classification by Sides

There are only 3 kinds of triangles which are possible if we consider only the sides.

1. All three sides are equal – These are called Equilateral triangles.

   1. We can intuitively see that all the 3 angles will also be equal.

   2. Since their sum has to be 180 degrees, each of the angles would be 60 degrees.

   3. This is a case where the sides determine the angles completely

2. Two of the sides are equal – These are called Isosceles triangle

   1. We can see intuitively that the 2 angles opposite the 2 equal sides would also be equal.

   2. These 2 equal angles can only be acute.

   3. The third angle can be acute or obtuse or right.

3. All three sides are unequal – These are called Scalene triangles

   1. Here all the 3 angles also would be unequal.

Classification by Angles

While considering sides, there is no restriction on the length of the sides. But while considering angles, there is a restriction that the total of the 3 angles cannot exceed 180 degrees.

We also need to keep in mind the classification angles as Acute, Obtuse and Right. It is obvious that only one of the angles in any triangle can be either Obtuse or Right. At least 2 angles in any triangle would be Acute.

Hence, we can classify triangles into 3 types

1. One of the angles is Obtuse – These are called Obtuse angled triangles

2. One of the angles is Right – these are called Right angled triangles

3. All the 3 angles are Acute – these are called Acute angled triangles.

Classification by both Angles & Sides

The sides and angles of a triangle are not totally independent in their measures. They affect one another. Hence we can also classify triangles jointly using both angles & sides.

A Scalene or an Isosceles triangle can be of 3 types – Acute, Obtuse and Right. An Equilateral triangle can only be Acute.

Hence, there are 7 types of triangles considering both sides & angles. They are presented in a visual form in Chapter 23.3.

1. Acute Isosceles Triangle

2. Obtuse Isosceles Triangle

3. Right Isosceles Triangle

4. Acute Scalene Triangle

5. Obtuse Scalene Triangle

6. Right Scalene Triangle

7. Acute Equilateral Triangle

Triangle Kit

A triangle kit made of triangles of all the 7 types can be used for assessing the understanding of students. Students should pick up any triangle and by visual inspection and informal modes decide the type of the triangle.

Informal mode means the use of paper folding & other means and not any formal ruler or protractor.