Question

ABCD is a trapezium in which AB || DC and E is the midpoint of
AD. A line is drawn through E parallel to AB intersecting BC at F.
Show that F is the midpoint of BC.​

Answer 1

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.