Question

In the given figure; AE bisects exterior angle CAD and AE is parallel to BC,
then $AB=AC$.

• A. True
• B. False

Answer 1

The correct option is A True

Since, $AE\parallel BC$,
thus, $\angle EAC=\angle ACB$ (Alternate angles)
Also, $\angle DAE=\angle EAC$ (AE bisects $\angle$ DAC)
$\angle DAC=\angle ACB+\angle ABC$ (Exterior angle is equal to sum of interior opposite angles)
$\angle ABC=\angle DAC-\angle ACB$
or $\angle ABC=\angle DAC-\angle EAC$
$\angle ABC=\angle DAE=\angle EAC=\angle ACB$
Now, In $△ABC$
Since, $\angle ABC=\angle ACB$
Hence, $AB=AC$ (Opposite sides of equal opposite angles are equal)