∆ABC is an isosceles triangle in which AB =AC and AE bisects∠CAD. Prove that AE \ \ BC

In the given figure, ∆ABC is an isosceles triangle in which AB = AC and AE bisects ∠CAD. Prove that AE \ \ BC.
image

Given ∆ABC is an isosceles triangle and AB = AC.
Also, AE bisects ∠CAD.
To prove AE || BC
Proof Given, AC = AB⇒ ∠B = ∠C
[∵ angles opposite to equal sides are equal]
Also, AE bisects∠CAD.
image
But these are alternate interior angles formed when the transversal AC cuts the lines AE and BC.
∴ AE || BC