Question

If any two sides of a triangle are unequal, then the larger side has the $.........$ angle opposite to it.

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

Answer 1

The correct option is A Greater

Given: $△ABC$, $AB>AC$

To Prove: $\angle ACB>\angle ABC$

Construction: Make a point D on $AB$ such that $AD=AC$ and join $DC$

In $△ACD$,
$AD=AC$
$\angle ACD=\angle ADC$ (Angles opposite to equal sides)

But $\angle ADC>\angle ABC$ (Exterior angle of the triangle is greater than the opposite interior angle)

Again, $\angle ACB>\angle ACD$ (D lies in interior of $\angle ACB$)
Thus, $\angle ACB>\angle ABC$