Question

ABCD is a trapezium In which AB|DC, BD is a diagonal and E is the
midpoint of side AD. A line is drawn through E parallel to AB
intersecting BC at F. Show that F is the midpoint of BC.
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Answer 1

Answer:

ANSWER

Given ABCD is a trapezium.

We have to prove, F is the mid point of BC, i.e., BF=CF

Let EF intersect DB at G.

In ΔABD E is the mid point of AD and EG∣∣AB.

∴ G will be the mid-point of DB.

Now EF∣∣AB and AB∣∣CD

∴ EF∣∣CD

∴ In ΔBCD, GF∣∣CD

⇒ F is the mid point of BC.