Question

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

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.