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Classification of Triangles
A polygon of 3 sides. It has 3 angles and 3 sides. So we classify triangles according to sides as well as according to angles. 
(i)    According to sides, the triangles are 
     (a)     Scalene Triangle : If all the sides of a triangle are unequal in length, it is called a scalene triangle. ABC is a scalene triangle.

(b)     Isosceles Triangle : If two sides of a triangle are equal. it is called isosceles triangle.
In ABC sides AB and AC are equal. 

(c)     Equilateral Triangle : If all the three sides of a triangle are equal, it is called equilateral triangle. AB = AC = BC, so ABC is an equilateral triangle. 

(ii)    According to angles, the triangles are 
       (a)     Acute angled Triangle : A triangle whose all angles are acute is known as an acute angled triangle. 

(b)     Right angled Triangle :  A triangle whose one of the angles is a right angle is called a right angled triangle. 

The side opposite to the right angle is called the hypotenuse and the other two sides are called the legs of the triangle. One leg (side) is perpendicular and other one is base. 

(c)      Obtuse angled Triangle : A triangle whose one of the angles is obtuse angle is called an obtuse angled triangle. 

Relation between Sides and Angles of a Triangle :  
(a)     The angles of a scalene triangle are unequal. 
(b)     In an isosceles triangle, two angles are equal. 
(c)     All the angles of an equilateral triangle are equal. Each angle is 60°. 
(d)     If two angles of a triangle are equal then  the sides opposite to them are also equal. 
(e)     A right angled triangle with two sides equal is called an isosceles right angled triangle.

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