Question

State true or false:

If the two angles of a triangle are unequal, then the greater angle has the larger side opposite to it.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $△ABC$, $\angle ACB>\angle ABC$
To Prove: $AB>AC$
Construction: Make a point D on $AB$ such that $\angle ACD=\angle ADC$ and join $DC$
In $△ACD$,
$\angle ACD=\angle ADC$
$AD=AC$ (Sides opposite equal angles)
But $AB=AD+DB$
thus, $AB>AD$
but $AD=AC$
Hence, $AB>AC$
Thus, sides opposite greater angles are larger