Question

ABCD is a parallelogram and D is the midpoint of AD. DL parallel to BE meets AB produced at F. prove that B is midpoint of AF and FB is equal to LF

Answer 1

ABCD is a parallelogram and E is the midpoint of AD.DLIIBE meets AB produced at F. prove  v

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 EBDF 

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