In triangle ABC , AB = BC; angle B is half of angle A. Is AB AC? then give reason for your answer.

In triangle, ABC, 

 AB = BC  [ given ]

⇒ ∠C = ∠A  [ angles opposite to equal sides are equal ]

now, ∠B = 1/2 ∠A  [ GIVEN ]

Now, ∠A + ∠B + ∠C = 180°  [ angle sum property ]

⇒  ∠A +  ∠A/2 +  ∠A = 180°

⇒  ∠A = 72° =  ∠C  ........(1)

Now,  ∠B = 36°  ..........(2)

In Δ ABC, we have

 ∠C >  ∠B  [ using (1) and (2) ]

⇒ AB > AC  [ In a triangle, side opposite to a greater angle is longer ]