ABCD is a p
To Prove: DF = 2DL
Given: ABCD is a parallelogram. E is the midpoint of AD. DL || EB meeting AB produced at F and BC at L.
Converse Midpoint Theorem: A line drawn through the mid-point of any side of a triangle and parallel to another side, bisects the third side.
Opposite sides of a parallelogram are parallel and equal to each other.
E is the midpoint of AD and EB || DF
B is the mid-point of AF [Converse mid-point theorem]
E and B are the midpoints AD and AF respectively
By mid-point theorem, we have,
EB = 1/2 DF.........(1)
Since EB || DL and BL || ED.
Opposite sides are parallel, and therefore, EBLD is a parallelogram.
EB = DL......(2) [opposite sides of a parallelogram are equal]
DL = 1/2 DF [L is the midpoint of DF]
LF = DL = EB
Therefore, EB = LF
Now, 1/2 DF = DL.
Hence, DF = 2 DL
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