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Definition of a triangle

A triangle is a plane closed figure bounded by three line segments.

The components of a triangle are sides, vertices and angles.

                                                      

Properties of triangles
The sum of the lengths of any two sides of a triangle, is always greater than the length of the third side.

Sum of the measures of the three angles of a triangle is always equal to 180°. 

Types of triangles
Classification of triangles is done in two ways:

1. Based on the types of angles contained in the triangle
2. Based on the length of the sides of the triangle

Based on the types of angles in a triangle

Right angled triangle: A triangle with one right angle ( = 90° ) is called a right angled triangle.

                                                           
Obtuse angled triangle: A triangle with one obtuse angle ( > 90° ) is called an obtuse angled triangle.

                                                         

Acute angled triangle: A triangle with all three angles as acute ( < 90° ) is called an acute angled triangle.

                                                           
Based on the length of the sides of a triangle

Equilateral triangle: A triangle whose all three sides are equal in length is called an equilateral triangle. In a equilateral triangle, each of the angles measure 60°.

                                                               

Isosceles triangle: A triangle whose two sides are equal in length, is called an isosceles triangle. In an Isosceles triangle, the angles opposite to each other are equal.

                                                                 
Scalene triangle: A triangle whose all sides are of different length, is called a scalene triangle.

                                                                     

Practice questions:

Question: In a right angled triangle, one of the acute angles measures 40°. Find the measure of the other acute angle.
( Answer: Sum of the measures of all the angles in a triangle = 180°
    Hence    90° + 40° + x = 180°
        X = 180° - 130°
        X = 50°
)

Question: Which of the following cannot be the measures of the angles of a triangle?
1. Angle A = 50°, Angle B = 30°, Angle C = 100°
2. Angle A = 20°, Angle B = 50°, Angle C = 10°
3. Angle A = 70°, Angle B = 110°, Angle C = 20°
4. Angle A = 90°, Angle B = 45°, Angle C = 45°
5. Angle A = 50°, Angle B = 60°, Angle C = 70°
( Answer: 2, 3 )

Question: Triangle ABC is an equilateral triangle. What is the measure of each of the angles of triangle ABC?
( Answer: 60°, 60°, 60° )

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