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Given : A triangle ABC in which BD = DC

to prove : AB = AC or ABC is an isosceles triangle .

Proof:

In triangle ABD and triangle ADC

AD = AD ( common)

∠ADB = ∠ADC (90° each)

BD = DC (given)

so Δ ABD ≡ ΔACD( by RHS)

So AB = AC (by cpct)

∴ Δ ABC is an isosceles triangle.

AD=AD.....(common)

angleADB=angleADC (both 90)

BD=CD (given)

ADB = ACD (ASA)

AB=AC (C.P.C.T)

Hence ABC is isosceles triangle..