Question

In the figure, AE bisects $\angle CAD$ and $\angle B=\angle C$ prove that $AE\left|\right|BC.$

Answer 1

Given : In $\Delta ABC,BA$ is produced and AE is he bisector of $\angle CAD$

$\angle B=\angle C$

To prove : $AE\left|\right|BC$

Proof : In $\Delta ABC,$ BA is produced

$\therefore Ext\angle CAD=\angle B+\angle C$

$\Rightarrow 2\angle EAC=\angle C+\angle C$

$(\because$ AE is the bisector of $\angle CAE)$

$(\because \angle B=\angle C$)

$\Rightarrow 2\angle EAC=2\angle C\Rightarrow \angle EAC=\angle C$

But these are alternate angles

$\therefore AE\left|\right|BC$