Question

if triangle ABC is an isosceles triangle such that AB is equal to AC.......

Answer 1

angle ADB=angADC,angABD=angaACD, line AB=lineAC so BD=CD

Answer 2

consider the given image.
Now,
In triangle ADB and Triangle ACD
AB = AC (given)
AD = AD (common)
and
angle ADB = angle ADC(both 90°)

Therefore, triangle ADB is congruent to triangle ADC by RHS congurence creteria.

therefore
BD = DC (by C.P.C.T)

Hence, AD bisects BC.