Question

if AC>AB and AD is the bisector of ∠A,show that ∠ADC>∠ADB.

Answer 1

Given: AC>AB

          and AD is bisector of angle A

⇒angleBAD = angle CAD = Angle A/2

 Also in triangle ABD

angle ABD+ angleBAD + angle ADB = 180 degree

⇒angle ADB = 180-angle ABD + Angle A/2

Now, angle ABD> angle ACD ...(∵ angle opposite to longer side is greater)

⇒angle ABD +angle A/2 > angle ACD + angle A/2

⇒180-angle ACD + angle A/2 > 180-angle ABD +angle A/2

⇒angle ADC > angle ADB