Question

in triangle ABC , AB=AC and D is any point on BC produced. show that AD>AB

Answer 1

In ΔABC, ∠ABC=∠ACB=θ (let)  [as AB=AC ⇒ΔABC is isosceles]

Now, we know that , in an isosceles Δ, the base angles are acute as only one obtuse angle can exist in a Δ.

Now ∠ACD= 180°-∠ACB     [linear pair]

so, in ΔACD , ∠ACD is the largest angle.

so, ∠ACD > ∠ADC

so, from triangle inequality, side opposite to the larger angle is gt the side opposite to the smaller angle,

so, AD > AC

but, AC=AB   [given]

so, AD > AB

Quad Erat Demonstrandum.

Answer 2

Here is your answer