Please solve question no.5.

Dear student, 
Given: ABCD is a parallelogram. E is the midpoint of AD and DL is parallel to EB. meets AB produced at F.
TPT: B is the midpoint of AF and EB = LF
proof:
in triangle ADF , 
E is the midpoint of AD and EB´┐╝ || DF 
therefore by the converse of mid point thm.
 B is the mid point of AF.
in triangle ADF,
E and B are the mid points AD and AF respectively
by the mid point thm EB = 1/2 DF.........(1)
since EB is parallel to DL and BL is parallel to ED.
EBLD is a parallelogram .
EB =DL......(2) [opposite sides of a parallelogram are equal]
DL = 1/2 DF i.e. L is the midpoint of DF.
LF = DL = EB
therefore EB = LF
Regards. 

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