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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. 8.30). Show that F is the mid-point of BC.

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.

  

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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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