D16.7. In the given AABC, D, E and F are pointson AB, BC and AC respec

1.	D16.7. In the given AABC, D, E and F are pointson AB, BC and AC respectively such that ADEF is aparallelogram, then prove that CF _ ADFA™ BD[CBSE SP 2011]
Answer» Given - ADEF is a parallelogram. To prove- CF/FA = AD/BD Proof-In triangle ABC, FE // AD ........(given) therefore,FE // AB ALSO, CF/FA = CE/EB .................(BY B.P.T) .........(i) now, DE // CF.........(given) therefore, DE // AC also,BE/EC = BD/AD.................(BY B.P.T) or,CE/EB = AD/BD.........(ii) comparing eq..(i) n (ii),,we get: CF/FA = AD/BD hence proved

D16.7. In the given AABC, D, E and F are pointson AB, BC and AC respectively such that ADEF is aparallelogram, then prove that CF _ ADFA™ BD[CBSE SP 2011]

Answer»

Given - ADEF is a parallelogram.

To prove- CF/FA = AD/BD

Proof-In triangle ABC,

FE // AD ........(given)

therefore,FE // AB

ALSO, CF/FA = CE/EB .................(BY B.P.T) .........(i)

now, DE // CF.........(given)

therefore, DE // AC

also,BE/EC = BD/AD.................(BY B.P.T)

or,CE/EB = AD/BD.........(ii)

comparing eq..(i) n (ii),,we get:

CF/FA = AD/BD

hence proved