EXERCISE 6.2 sum no.4 (class 10th )

              EXERCISE 6.2
SUM 4.  In a figure,DE∥AC and DF∥ AE, prove that BE/FE=BE/EC.
Solution:- 
Given:- DE∥AC and DF∥ AE
To Prove :- BE/FE=BE/EC

Proof:-
In △ABC 
DE∥AC 
Because (if a line is drawn parallel to one side of triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.)

 BE/EC=BD/DA        .......(1)

and, In △AEB
DF∥ AE
Because  (if a line is drawn parallel to one side of triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.)

BF/FE= BD/DA            ......(2)
   
From (1) and (2)

 BE/FE=BE/EC

 Hence proved 

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