Question

The following statement is true (T) and false (F)?
Difference of any two sides of a triangle is equal to the third side.

• A. True
• B. False

Answer 1

The correct option is B False

Cut off $AD=AB$, join $BD$

$\angle 2=\angle 4$

Exterior $\angle 1>\angle 4$ [ Exterior angle is greater than each of the interior angles ]

Exterior $\angle 2>\angle 3$

$\Rightarrow$ $\angle 1>\angle 3$

$\Rightarrow$ $BC>DC$ [ Side opposite greater angle is greater ]

$\Rightarrow$ $BC>AC-AD$ [ $DC=AC-AD$ ]

$\Rightarrow$ $BC>AC-AB$ [ $AD=AB$ ]

$\Rightarrow$ $BC>AC-AB<BC$

Similarly, $BC-AC<AB$ and $BC-AC<AC$

Hence, the difference of any two sides of a triangle is less than the third side.

$\therefore$ The given statement is false.