Triangle inequality theorem

As we all are very well aware that geometry provides lots of shapes and figures to solve out the problems that are related to mathematics. In mathematics, triangle is a shape that provides the various concepts to solve the problem. Triangle inequality is one of them, which states that the sum of lengths of any two sides of the triangle must be greater than or equal to the length of third side. Euclidean geometry says that triangle inequality is a theorem about the distance. In simple definition of the triangle inequality theorem we can say that the total of any two sides of triangle must be greater than the third side of the triangle. If in case the above theorem is not applied at the time of triangle creation then that figure is not considered as a Triangle. This theorem helps the student of Grade IX to understand the concept.
Suppose a triangle has three sides which named as A, B and C. Now we check that the given triangle is a complete triangle or not by applying the inequality theorem. The Triangle Inequality theorem says that:
B + C > A,
A + B > C,
C + A > B,
If in the given triangle, available values satisfy the above combination or pairs of inequality then the triangle can be considered as complete triangle. In study of Triangle of geometry, we generally study three types of triangle which are equilateral triangle, isosceles triangle and right angle. In all types of triangle we can easily see the operation of triangle inequality theorem. (know more about icse syllabus 2013 , here)
Example: Can a triangle have the side lengths of side 1 = 4cm, side 2 = 8 cm and side 3 = 2cm?
Solution: Now we need to apply the triangle inequality theorem. By applying the Triangle inequality theorem we create three combinations that are given below:
Side 1 + side 3 > side 2,
  4 + 2 > 8,
The first equation get false then we can say that the above given sides are not able to form the triangle.
In the next session we will discuss about Basic constructions.