Triangle Inequality Theorem

“Length of any side of a triangle is less than the sum of the lengths of other two sides”

a < b+c            b < a+c            c < a+b                                    ---(1)

From this we can easily derive the following:

a > b~c            b > a~c            c > a~b                                    ---(2)

From (1) and (2),

b~c < a < b+c             a~c < b < a+c             a~b < c < a+b

This theorem is most important for competitive exams. You can find Geometry-12 problem on this blog, which is based on this theorem.