In the figure, ABCD is a parallelogram in which E is midpoint of AD. D

1.	In the figure, ABCD is a parallelogram in which E is midpoint of AD. DF II EB, meeting AB produced in F and BC at L. Prove that DF=2DL.
Answer» 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.

In the figure, ABCD is a parallelogram in which E is midpoint of AD. DF II EB, meeting AB produced in F and BC at L. Prove that DF=2DL.

Answer»

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.