prove that in triangle ABC, if AB AC and D is any point on the side BC, then AB AD - Maths - Triangles

Question

prove that in triangle ABC, if AB>AC and D is any point on the
side BC, then AB>AD

Manbar Singh · Accepted Answer

In ∆ABC, we have      AB > AC⇒∠ACB > ∠ABC   Angle opposite to greater side is longer    
1We know that, measure of an exterior angle of a ∆ is always greater than each of the interior opposite angle
    ∠ADB > ∠ACD⇒∠ADB > ∠ACB     
2From 1 and 2, we get∠ADB > ∠ABC⇒∠ADB > ∠ABD⇒AB > AD

prove that in triangle ABC, if AB>AC and D is any point on the side BC, then AB>AD