Question

In the given figure, AE bisects ∠CAD and ∠B= ∠C. Prove that AE || BC.

Answer 1

In the given problem, AE bisectsand

We need to prove

As,is bisected by AE

=2=2 ..........(1)

Now, using the property, “an exterior angle of a triangle in equal to the sum of the two opposite interior angles”, we get,

()

(using 1)

Hence, using the property, if alternate interior angles are equal, then the two lines are parallel, we get,

Thus,

Hence proved.