Question

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

• A. Smaller
• B. Larger
• C. May be smaller may be larger
• D. The side will be equal to one of the opposite sides

Answer 1

The correct option is A Smaller

Let, In $△ABC$, $\angle ACB>\angle ABC$
To Prove: $AB>AC$
Construction: Make a point $D$ on $AB$, such that $\angle ACD=\angle ADC$ and join $DC$
Now, in $△ACD$,
$\angle ACD=\angle ADC$
$\therefore AD=AC$ (Sides opposite to equal angles)

But $AB=AD+DB$
thus, $AB>AD$
Hence, $AB>AC$ [as $AD=AC$]

Thus, sides opposite smaller angles in a triangle are smaller.