Question

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

Answer 1

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

Answer 2

In ∆ ABC, 
AB = AC
Angle BAD = Angle CAD
AD = AD 
Therefore, ∆ADB ~ ∆ADC