ABCD is a trapezium in which
, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see figure). Show that F is the mid-point of BC.
Solution:
(Given) (1)
(Given) (2)
From (1) and (2), we have
In
, E is the mid-point of AD and
(Given)
Therefore, by converse of mid-point theorem, O is the mid-point of BD.
(The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.)
In
, O is the mid-point of BD and
. (Proved above)
Therefore, by converse of mid-point theorem, F is the mid-point of BC.
(The line drawn through the mid-point of one side of a triangle, parallel to another side bisects the third side.)
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