Triangle Inequality Theorem:

The Triangle Inequality Theorem says:

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

i.e.,

a + b > c

b + c > a

a + c > b

Example 1) 8cm , 3cm , 4cm

a = 8 cm, b = 3 cm , c = 4 cm

a + b = 8 + 3 = 11 > c (4)

b + c = 3 + 4 = 7 ≮ a(8)

a + c = 8 + 4 = 12 > b(3)

8cm , 3cm , 4cm line segments can not construct a triangle.

Example 2) 6cm , 5cm , 9cm

a = 6 cm, b = 5 cm , c = 9 cm

a + b = 6 + 5 = 11 > c (9)

b + c = 5 + 9 = 14 > a(6)

a + c = 6 + 9 = 15 > b(5)

6cm , 5cm , 9cm line segments can construct a triangle.