# 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.

M mansi

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 $\triangle$ABD,

E is the midpoint of AD.                (Given)

EG || AB                          (Given)

By converse of  midpoint theorem,

G is the midpoint of BD.

In $\triangle$BCD,

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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