given that ,
L is the midpoint of side AB of ΔABC and N is the point on AC i.e. AN = 2CN .
We have to prove - AM = CN
in Δ ANB .
By using convs. of midpoint theoram .
M is also a midpoint of AN
⇒ AM = MN
AN = 2CN
also , AM + MN = 2CN
AM + AM ( because AM = MN ) = 2 CN
2AM = 2 CN
.'. AM = CN ( Proved ).................