Question

D is any point situated on side AC of triangle ABC with AB=AC. show that BD is greatervthan CD

Answer 1

Given AB = AC in triangle ABC

So,

∠ ABC  = ∠ ACB        (angles opposite to equal sides are equal)

⇒∠ABC  = ∠ABD + ∠DBC

⇒∠ABC > ∠DBC

⇒∠ACB > ∠DBC  [As, ∠ABC = ∠ACB]

⇒∠DCB > ∠DBC

⇒BD > CD   (side opposite to greater angle is longer)