Question

In given figure , ABC is a triangle in which AB= AC .fo be a point on Bc produced, prove that AD > AC.​

Answer 1

$Answer$

Given : AB=AC

To prove : AD>AB

Proof :

In ΔABC,

∠ABC=∠ACB=θ (say) [as AB=AC⇒ΔABC is isoceles]

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

Now, ∠ACD=180 ° −∠ACB (linear pair)

So, in ΔACD,∠ACD is the largest angle

So, from triangle inequality, side opposite to the larger angle is greater than the side opposite to the smaller angle

So, AD>AC

but, AC=AB (given)

⇒AD>AB

Hence proved.