Question

In triangleABC , AB=AC and AD bisects angle A. Show that triangle ADB ~ triangle ADC

Answer 1

In ∆ ABC,
AB = AC(Given)
AD = AD (Common)
Therefore, ∆ADB ~ ∆ADC
(By SAS)

Answer 2

In triangle ADB and triangle ADC
     AB=AC[given]
  angle DAB= angle DAC [bcoz AD bisects angle A]
  AD=AD [common]
So,by SAS
  triangle ADB ~ triangle ADC
    Hence showed
see picture for more explanation