Question

ABC IS A TRIANGLE IN WHICH L IS THE MIDPOINT OF AB AND N IS A POINT ON AC SUCH THAT AN =2 CN. A LINE THROUGH L PARALLEL TO BN,MEETS AC AT M.PROVE THAT AM=CN.

Answer 1

Given  ABC is a triangle .L is the midpoint of AB. AN =2CN
To prove  AM = CN

In ∆ ABN, we haveLM∥BN  and L is the midpoint of AB .
Hence M is the midpoint of AN (converse of midpoint theorem)
∴AM=MN
Now it is given  AN = 2 CN
⇒AM+MN =2CN
⇒AM+AM =2CN    
⇒2AM=2CN
⇒AM =CN  proved
i hope it helps