Question

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

• A. May be less or more
• B. More
• C. Equal
• D. Less

Answer 1

The correct option is D Less

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, from Isosceles triangle has two equal angles,
$\angle ADC=\angle ACD$
Thus, in $△DCB$,
$\angle BCD>\angle BDC$ (Side opposite greater angle is larger)
Thus, $BD>CD$
$BA+AD>CD$ (Since, $AC=AD$)
$BA+AC>CD$
$AC>CD-BA$
Thus, difference in two sides is less than the third side.