In the figure, if LM || CB and LN || CD, prove that \(AM\over AB\) = \(AN\over AD\).

Solution :

In triangle ABC,

Given,        LM || CB

By Basic proportionality theorem, we have

\(AM\over AB\) = \(AL\over AC\)           ……..(1)

In triangle ACD,

Given,        LN || CD

By Basic proportionality theorem, we have

\(AL\over AC\) = \(AN\over AD\)           ……..(2)

From (1) and (2), we obtain that

\(AM\over AB\) = \(AN\over AD\)