Question

In the given figure, AB = AC and B – C – D. Prove that : AD > AB.

Answer 1

Step-by-step explanation:

Given :– AB = AC,

To prove :– AD > AB

Proof :– We know that the angles oppositeto equal sides are equal.

∴ AC = AB ⇒ ∠ACB = ∠ABC. -----(i)

In ∆ACD , the side DC has been produced to B.

∴ ∠ACB > ∠ADC [ext.∠ is greater than

int. opp. ∠s]

⇒∠ABC > ∠ADC [using (i)]

⇒∠ABD > ∠ADB [∵ ∠ABC = ∠ABD and

∠ADC = ∠ADB]

⇒AD > AB