Question

In the given figure, if ABCD is a trapezium in which AB║CD ║ EF then prove that \(\frac{AF}{ED}=\frac{BF}{FC}.\)

Answer 1

Given

AB II CD II EF

To prove: \(\frac{AE}{ED}=\frac{BF}{FC}\)

Construction:- Join BD to 1/2 

intersect EF at G. 

Proof:- in ∆ ABD 

EG II AB ( EF II AB )

\(\frac{AE}{ED}=\frac{BG}{GD}\) ( by BPT )___(1)

In ∆DBC

GF II CD ( EF II CD )

\(\frac{BF}{FC}=\frac{BG}{GD}\) ( by BPT )_____(2) 1/2 

from (1) & (2)

\(\frac{AE}{ED}=\frac{BF}{FC}\)