Question

In the given figure, ray AE bisects exterior $\angle CAD$ and ray AE is parallel to side BC. Hence, $AB=AC.$
State whether the above statement is true or false.

Answer 1

Given, $AE\parallel BC$
hence, $\angle EAC=\angle ACB$ ...(Alternate angle to parallel lines)
Also, $\angle DAE=\angle ABC$ ....(Corresponding angles of parallel lines)
We know, AE bisects $\angle DAC$
$\therefore \angle EAC=\angle DAE$
thus, $\angle ACB=\angle ABC$
$\therefore △ABC$ is an isosceles triangle