(Q19) In the given figure, DE ∥ AC and DF ∥ AE. Prove that
BF
FE
 =
BE
AC
ABCDFE

In ∆ABC, DE ∥ AC

Hence
EC
 =
BD
 ....(1)

[∵ A line drawn parallel to one side of a triangle divides the other two sides in the same ratio - Basic proportionality theorem]

Also in ∆ABE, DF ∥ AE

Hence
BF
 =
DA
 ....(2)
From (1) and (2),
FE
 =
BE

Hence Proved.