in triangle ABC d,e and f are points on ab. bc and ac respectively such that adef is a parallelogram the prove that cf/ fa = ad/ bd
Answers
Answered by
40
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
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
Answered by
21
I hope the figure is correct.
Attachments:
Similar questions