E is the mid-point of the side AD of the trapezium ABCD with AB || DC. A line through E drawn parallel to AB intersect BC at F. Show that F is the mid-point of BC. [Hint: Join AC]



Given,


ABCD is a trapezium in which AB||DC.


Joining diagonal AC, which intersects EF at O.


In ΔADC, E is mid-point of AD and OE || CD.


By mid-point theorem, O is mid-point of AC.


Similarly,


In ΔCBA, O is mid-point of AC and OF||AB.


F is mid-point of BC by Mid-point Theorem.


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