Q : 4     ABCD is a trapezium in which  \small AB\parallel 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. \small 8.30). Show that F is the mid-point of BC.

            

Answers (1)

Given: ABCD is a trapezium in which  \small AB\parallel 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. \small 8.30).

To prove: F is the mid-point of BC.

   In \triangleABD,

      E is the midpoint of AD.                (Given)

               EG || AB                          (Given)

  By converse of  midpoint theorem,

                       G is the midpoint of BD.

 

In \triangleBCD,

      G is mid point of BD.                (Proved above)

               FG || DC                          (Given)

  By converse of  midpoint theorem,

                       F is the midpoint of BC.

 

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