(we have drawn an triangle ABC and AD is the altitude)
Given : A triangle ABC in which BD = DC
to prove : AB = AC or ABC is an isosceles triangle .
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.