Question

Sum of any two sides of a triangle is $..........$ than the third side.

• A. Greater
• B. Lesser
• C. Equal
• D. May be greater or lesser

Answer 1

The correct option is A Greater

Let $ABC$ be a triangle,

We can extend $BA$ past $A$ into a straight line,

Then there is a point $D$ such that $DA=CA$
Therefore, the Isosceles triangle has two equal angles.
$\angle ADC=\angle ACD$

Thus, in $△DCB$,
$\angle BCD>\angle BDC$ (Side opposite greater angle is larger)

Thus, $BD>CB$
$BA+AD>CB$ (Since, $AC=AD$)
$BA+AC>CB$

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