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