Question

If two sides of a triangle are unequal, the greater side has the greater angle opposite to it. State whether the given statement is true or false.

• A. True
• B. False

Answer 1

The correct option is A

True

Let consider a triangle ABC in which AB > AC.

From AB, cut AD = AC. Join C and D.

In $\Delta$ACD:

AC = AD (by construction) --------(1)

$\angle$ACD = $\angle$ADC (Angle opposite to equal side) --------(2)

In $\Delta$BDC

Ext . $\angle$ADC > $\angle$B (Ext. angle always greater than each of its interior opposite angles) --------(3)

$\angle$ACD > $\angle$B ------------ From (2) and (3)

Hence, $\angle$ACB > $\angle$B

Therefore, $\angle$ACB > $\angle$ACD > $\angle$B

Thus, given statement is true.