# Please solve question no.5.

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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