Question

In a triangle ABC,D,E and F are points on AB,BC and AC respectively such that ADEF is a parallogram,then prove that CF/FA=AD=BD.

Answer 1

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