Question

D is any point on side AC of a ∆ABC with AB = AC. Show that CD < BD.

Answer 1

Given in triangle ABC, D is any point on side AC such that AB = AC.

To proof that CD < BD or BD > CD

To proof: AC = AB   ...[Given]

∠ABC = ∠ACB  ...(i) [Angle opposite to equal sides are equal]

In triangle ABC and triangle DBC,

∠ABC > ∠DBC   ...[∠DBC is a internal angle of ∠B]

∠ACB > ∠DBC  ...[From equation (i)]

BD > CD   ...[Side opposite to greater angle is longer]

CD < BD