D is any point on side AC of a ABC with AB = AC. Show that CD < BD.
Given: ABC is a triangle and D is any point on AC.
AB = AC
To prove: CD < BD.
Proof: In ABC
AB = AC (Given)
ABC = ACB (angles opposite to equal sides are equal)
In ABC and DBC
ABC > DBC
ACB > DBC
BD > CD (Side opposite to greater angle is larger)
CD < BD
Hence proved.