Question

In the given figure; AE bisects exterior angle CAD and AE is parallel to BC.

Prove that: AB = AC.

Answer 1

Since AE || BC and DAB is the transversal.
∴ ∠DAE = ∠ABC = ∠B .......[Corresponding angles]
Since AE || BC and AC are the transversals.
∴ ∠CAE = ∠ACB = ∠C ......[Alternate angles]
But AE bisects ∠CAD,
∴ ∠DAE = ∠CAE
⇒ ∠B = ∠C
⇒  AB = AC .......[Sides opposite to equal angles are equal]