Question

A STRAIGHT LINE SEGMENT AB IS BISECTED AT C AND PRODUCED TO D . SHOW THAT AD + BD = 2CD

Answer 1

so AC = CB
AD = AB + BD
AD + BD = AB + 2BD
AD + BD = AC + BD + CB + BD
AD + BD = CB  + BD + CB + BD   [SINCE AC = CB]
AD + BD = CD + CD
AD + BD = 2CD    HENCE PROVED

Answer 2

sice C bisects
so AC = CB
AD = AB + BD
AD + BD = AB + 2BD
AD + BD = AC + BD + CB + BD
AD + BD = CB  + BD + CB + BD   (since AC = CB)
AD + BD = CD + CD
AD + BD = 2CD   
so proved