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\(ABCD\) is a trapezium in which \(AB || DC\), \(BD\) 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 Fig.). Show that \(F\) is the mid-point of \(BC\).
 
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This is a self assessment task. Solve this question and assess the solution steps after the completion of test on your own.