1. TRIANGLE INEQUALITY THEOREM

2. 5+15 >12 or 20>12 5+12 >15 or 17>15 5
Triangle inequality theorem states that the sum of the lengths of any
two sides of a triangle is greater than the third side. 5 12 15 5 12 15
5+15 >12 or 20>12
5+12 >15 or 17>15 5 12 15
12+15 >5 or 27>5
Therefore we can see, in a triangle if we take sum of any two side ,
it is always greater than third side.

3. We can use triangle inequality theorem to find if a triangle can be formed
given 3 sides.
Instead of checking triangle equality by all sides in the triangle check only with
two smaller sides
i.e Sum of two smaller sides is greater than third side
Example1: Can a triangle be formed given sides 7cm , 5cm and 10 cm
Solution
The two smaller sides are 5 cm , 7cm and third side is 10cm
The sum of two smaller sides are =12 cm
If sum of two smaller sides greater than third side then triangle be formed
> 10
sum of two smaller sides > third side then triangle
Therefore triangle can be formed using the given sides.

4. Example2: Can a triangle be formed given sides 5cm , 8cm and 11 cm
Solution
The two smaller sides are 5 cm , 8cm and third side is 11cm
The sum of two smaller sides are =13 cm
If sum of two smaller sides greater than third side then triangle be formed
< 11
sum of two smaller sides > third side then triangle
Therefore triangle cannot be formed using the given sides.

5. Example3: Can a triangle be formed given sides 4cm , 10cm and 6 cm
Solution
The two smaller sides are 4 cm , 6cm and third side is 10cm
The sum of two smaller sides are =10 cm
If sum of two smaller sides greater than third side then triangle be formed
= 10
sum of two smaller sides = third side then triangle
Therefore triangle cannot be formed using the given sides.

6. Try These Can a triangle been drawn using the following measurements:
5cm, 3 cm and 4 cm
13cm, 4cm and 19cm