Question

ABCD is a trapezium where ABIIDC is midpoint of AD. a line drawn from E, parallel to AB, meet BC at point F. prove that f is midpoint of BC.

Answer 1

Given,

ABCD is a trapezium in which AB || DC, BD is a
diagonal and E is the mid-point of AD and a line is drawn through E parallel to
AB intersecting BC at F such that EF||AB.


To Show:

F is the mid-point of BC.


Proof:

Let EF
intersected BD at G.



In ΔABD,

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



we get, G is the mid point of BD

(by Converse of mid
point theorem)



Similarly,

In ΔBDC,

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



Thus, F is the mid point of BC

 (by Converse of mid point theorem)

_____________________________________________________________

 Hope this will help you...

Answer 2

hope this helps you out