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 ]

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