Question

Please answer question no. 17

Answer 1

Answer:

Given : ABCD is a parallelogram. E is the midpoint of AD and DL II EB. DL meets AB produced at F.

To Prove : 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