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.<p></p>

In△DAB,Let lineEFintersect sideDBatG, such thatE−G−Fis a line.Eis the midpoint of sideADandEG∥AB.By converse of midpoint theorem,Gis the midpoint of sideBD (1)AB∥DCgivenAB∥EFgiven∴AB∥DC∥EF(2)In△BDC,Gis the midpoint of sideBD...from (1)andDC∥GFfrom (2)By converse of midpoint theorem,Fis the midpoint of sideBC

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Question:

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.

Solution: