Triangle

What is a triangle?

A simple closed curve or a polygon formed by three line-segments (sides) is called a triangle.

$What is a Triangle$

The above shown shapes are triangles. The symbol of a triangle is ∆.

A triangle is a polygon with three sides. In the given figure ABC is a triangle. AB, BC and CA are its sides. The point where two sides meet is called its vertex. A, B, C are its vertices. There are many types of triangles. Triangles can be classified on the basis of sides and angles. Some triangles which are given below have been classified on the basis of their sides.

$Triangle is a Polygon$

A triangle has

three line-segments or sides
three vertices
three angles

There are six types of triangles, 3 with respect to sides and 3 with respect to angles.

Three types of triangle with respect to sides

(i) A triangle having all the three line-segments or sides unequal is called a scalene triangle.

$Scalene Triangle$

Scalene Triangle

A triangle which has no equal sides is called a scalene triangle. ABC in the given figure is a scalene triangle, its sides AB, BC and CA are of different lengths.

(ii) A triangle having a pair of its sides or two line-segments equal is called an isosceles triangle.

Here AB = AC.

$Isosceles Triangle$

Isosceles Triangle

A triangle which has two equal sides is called an isosceles triangle. ABC in the given figure is an isosceles triangle, its sides AB and AC are equal.

(iii) A triangle having all the three line-segments or sides equal is called an equilateral triangle.

Here AB = BC = CA.

$Equilateral Triangle$

Equilateral Triangle

A triangle which has three equal sides is called an equilateral triangle. ABC in the given figure is an equilateral triangle, its all sides are equal. AB = BC = CA.

Types of triangle with respect to angles

(i) A triangle in which all the three angles are acute is called an acute angled triangle.

∠ABC, ∠ACB and ∠BAC are all acute angles.

$Acute Angled Triangle$

Acute Angled Triangle

(ii) A triangle in which one of the three angles is a right angle is called a right angled triangle.

∠ABC = one right angle.

$Right Angled Triangle$

Right Angled Triangle

(iii) A triangle where one of the three angles is more than a right angle (or is an obtuse angle) is called an obtuse angled triangle.

∠ABC is an obtuse angle.

$Obtuse Angled Triangle$

Obtuse Angled Triangle

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