Question

In the given figure, E is the mid point of side AD of trapezium ABCD with AB II CD, EF II AB. A line through E parallel to AB meets BC in F. Show that F is the mid point of BC.

Answer 1

Given :-
ABCD is a trapezium

E is the midpoint of AD and AB║CD, EF║AB

To be Proof :-
F is the midpoint

Construction : Join AC to intersect EF at point G

PROOF :

EF║DC         (given)

⇒ EG║DC

Since,

E is the midpoint of AD

∴ G is the midpoint of AC  

[ By converse of midpoint theorem ]

In ΔABC,

FG║AB                  [ ∵ As EF║AB ]

G is the midpoint of AC

∴ F is the midpoint of BC

Hence,
Proved