\( E \) is the mid-point of the side \( A D \) of the trapezium \( A B C D \) with \( A B \| D C...

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\( E \) is the mid-point of the side \( A D \) of the trapezium \( A B C D \) with \( A B \| D C \). A line through \( E \) drawn parallel to \( A B \) intersects \( B C \) at \( F \). Show that \( F \) is the mid-point of \( B C \).
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