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. 8.30). Show that
F is the mid point of BC.
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Answer 1

Answer:

Step-by-step explanation:

Solution:

Given that,

ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD.

To prove,

F is the mid-point of BC.

Proof,

BD intersected EF at G.

In ΔBAD,

E is the mid point of AD and also EG || AB.

Thus, G is the mid point of BD (Converse of mid point theorem)

Now,

In ΔBDC,

G is the mid point of BD and also GF || AB || DC.

Thus, F is the mid point of BC (Converse of mid point theorem)