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

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.

But these are alternate interior angles formed when the transversal AC cuts the lines AE and BC.

∴ AE || BC