question number 18 

Hi, here is your answer

sol:

Given: ABCD is a trapezium.

To Prove: DE/EB = CE /EA

Construction: Draw EF || BA || CD, intersecting AD in F.

Proof:
 
FE || AB (Given)
 
DE/EB = DF/FA [According to basic proportionality theorem] --------- (1)
 
FE || DC (Given)

CE/EA = DF/FA [According to basic proportionality theorem] --------- (2)
 
From (1) and (2), we get
 
DE/EB = CE/EA
 
So, diagonals of a trapezium divide each other proportionally.