In the adjoining  figure, ∆ABC is an isosceles triangle in which AB = AC. Also, D is a point such that BD = CD.
Prove that AD bisects ∠A and ∠D

Figure

.Given:ABC is an isosceles triangle.AB=ACBD =CD To prove:AD bisects A and D.Proof:Consider ABD and ACD:AB=AC    (given)BD=CD    (given)AD=AD     (common) By SSS congruence property:ABD ACD =>BAD=CAD     (by cpct)=>BDA=CDA      (by cpct)

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