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in the given figure AB = AC.D is the point in the interior of triangle ABC. Such that angle DBC = angle DCB. Prove that AD bisects angle BAC of triangle ABC

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 Given:AB=AC,D interior point on triangle ABC.Angle B =Angle C.

To prove:AD bisects angle A.

Proof: Consider triangle ABD and ADC

  AD=AD(common)

  AB=AC(given)

  angle B=angle C

So by SSA we can prove that triangle ABD is congruent to triangle ADC

 By C.P.C.T. we can prove that AD is bisector of angle A .

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