In the given figure, \(LM||AC\) and \(LN||AM\), prove that \(\frac{BN}{NM} = \frac{BM}{MC}\).
Proof:
In \(\Delta ABC\),
\(LM ||\)
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
\(\frac{BM}{MC} =\) - - - - (1)
In \(\Delta AEB\),
\(DF ||\)
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
\(\frac{BF}{FE} =\) - - - - (2)
From (1) and (2) we get,
Hence proved.