Question

The greater side of a triangle has greater angle opposite to it.

• A. True
• B. False

Answer 1

The correct option is A True

In $△ABC,$

$AC>AB$

From $AC$, cut off $AP$ such that $AP$ equals $AB$. Join $B$ and $P$.

In $△ABP,$

$\Rightarrow$ $\angle ABP=\angle APB$ [ Base angles of equal sides are also equal ] ---- ( 1 )

$\Rightarrow$ $\angle APB=\angle ACB+\angle PBC$ [ By exterior angle theorem ] --- ( 2 )

$\Rightarrow$ $\angle APC>\angle ACB$ [ From ( 2 ) ] ----- ( 3 )

$\Rightarrow$ $\angle ABP>\angle ACB$ [ From ( 1 ) and ( 3 ) ] ----- ( 4 )

But $\angle ABC>\angle ABP$ [ $\angle ABC=\angle ABP+\angle PBC$ ] ----- ( 5 )

From ( 4 ) and ( 5 )

$\therefore$ $\angle ABC>\angle ACB$ ----- Hence proved

$\therefore$ The greater side of a triangle has greater angle opposite to it.