Question

In Triangle ABC, AD bisects angle BAC and AB = AC. Prove that angle ADB = angle ADC = 90 degree

Answer 1

Answer:

In ∆ABD and ∆ACD,

AB=AC (given)

AD=AD (common)

BD=CD (given AD is the bisector)

So, ∆ABD is congruent to ∆ACD on SSS rule.

By CPCT, angle ADB = angle ADC

But BDC is a straight line, so angle ADB+angle ADC = 180°

Which implies angle ADB=90°

Hence proved.