# 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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i cannot get u .. are you asking that ab= ac... if ur askin dis den

the answer is no ab can't be = ac if /_b=1/2 /_a because in dis condition we can say that bc=ac and it is only possible if the triangle is equilateral .... and in an eq triangle all angles are 60 degree but it is given that /_b=1/2 /_a .. so this is nt possible

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i cannot get u .. are you asking that ab= ac... if ur askin dis den

the answer is no ab can't be = ac if /_b=1/2 /_a because in dis condition we can say that bc=ac and it is only possible if the triangle is equilateral .... and in an eq triangle all angles are 60 degree but it is given that /_b=1/2 /_a .. so this is nt possible

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