Meaning of the Triangle

Geometric figures are congruent if they have the same shape and the same size. We shall learn some properties of geometric figures that are of the same shape but not necessarily of the same size. Such figures are said to be similar. It is obvious that the congruent figures are similar but the converse is not necessarily true.
         
A triangle is a three-sided polygon. In fact, it is the polygon with the least number of sides. We write D ABC instead of writing “Triangle ABC”.

Meaning of the triangle - Properties:

We know already two important properties of a triangle,

            (i) The sum of the angles of a triangle is 180 degree
            (ii) The sum of any two sides of a triangle is greater than the third side.
Observe that one of these statements is about the angles of a triangle, while the other is about the sides of a triangle.

1. Classify the following triangles on the basis of the sides into,
Scalene triangle:
A triangle in which all the sides are of different lengths and no two sides are equal, the triangle is called a scalene triangle.


Isosceles triangle:
A triangle in which two sides are of equal lengths is called an isosceles triangle.



 Equilateral triangle
A triangle in which all the three sides are of equal lengths is called an equilateral triangle.



2. Classify the following triangle on the basis of the angles into,

Acute angled triangle
A triangle whose all angles are acute is called an acute angled triangle or simply an acute triangle
    
 Right angled triangle:
A triangle whose one of the angles is a right angle is called a right angled triangle, or simply a right triangle.
    
Obtuse angled triangle:
A triangle one of whose angles is obtuse is called an obtuse angled triangle or simply an obtuse triangle.

Meaning of the triangle - Example problems:

Meaning of the triangle problem 1:
Two angles of a triangle measure 55 degree and 85 find the measure of the third angle.



Solution:
            Let the measure of the third angle be x degree.
            We know that the sum of the angles of a triangle is 180 degree
                        55 + 85 + x = 180
                        140 + x = 180
                                    X = 180 – 140
                                        = 40


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Meaning of the triangle problem 2:
            The angles of a triangle are in the ratio 4: 2:3, Find the angles of a triangle.
Solution:
            Let the angles of the given triangle be 4x, (2x), (3x).
            The sum of the angles of a triangle is 180 degree
                        4x + 2x + 3x = 180
                                    9x = 180
                                    X = 180 / 9
                                    X = 20
            4x = 4 * 20 = 80
            2x = 2 * 20 = 40
And     3x = 3 * 20 = 60

The angles of the triangle are 80, 60, 40