triangle inequality theorem

Hello students, in this session we are going to discuss the triangle inequality theorem. This theorem defines that the sum of any two sides will always be greater than the third side or we can say that the only one side is shorter than the other two sides; meaning is same in both the scenario. The theorem is - If we have x, y and z sides for the any triangle then,
x + y > z,
y + z > x,
x + z > y,
It is to be noted that if any one side of triangle is greater than the other two sides then we cannot construct the triangle. Also the triangle inequality theorem says same. for more information visit here
We can see this by an example:
Is a triangle with the sides 6cm, 7cm and 8cm possible?
Solution: Sum of 2 sides is always greater than the third side.
Then according to theorem
x + y > z,
y + z > x,
x + z > y,
6 + 7 > 8,
7 + 8 > 6,
8 + 6 > 7,
We can see that in above example the sum of 2 sides is greater than the third side. So, the triangle is possible.
Is a triangle with 3 cm, 4 cm and 13 cm possible?
Solution:
3 + 13 > 4
4 + 13 > 3
3 + 4 >12
In above example the last inequality is false, so, the triangle is not possible
Note:
 i) If in two triangles the two sides are congruent, then the triangle that have larger third side will keep larger included angle.
ii) If in two triangles the two sides are congruent, then the triangle that have larger included angle will keep a larger side.
Central Board of Secondary Education Grade XII students can practice by reading this discussion.

In upcoming posts we will discuss about Triangle congruence relationships and Permutations and combinations. Visit our website for information on Circumference Formula of a Circle