Question

ABC is a triangle in which L is mid point of AB and N is a point on AC such that AN=2CN.A line through L, parallel to BN, meets AC at M .prove that : AM=CN

Answer 1

In triangle ABN,
as L is the midpoint of AB and lm is parallel to BN .
therefore M is the Midpoint of AN
Now,
AN=2CN(GIVEN)-equation(1)
Here,
as M is the mid point of AN.
Therefore AN=2AM-equation(2)
Now,From equation (1) and (2)
(AN=2CN)=(AN=2AM)
Therefore AM=CN
                              Hence proved
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Answer 2

In triangle ABN, as L is the midpoint of AB and lm is parallel to BN . therefore M is the Midpoint of AN Now, AN=2CN(GIVEN)-equation(1) Here, as M is the mid point of AN. Therefore AN=2AM-equation(2) Now,From equation (1) and (2) (AN=2CN)=(AN=2AM) Therefore AM=CN Hence proved