E is the mid-point of the side AD of the trapezium ABCD with AB || DC. A line through E drawn parallel to AB intersect BC at F. Show that F is the mid-point of BC. [Hint: Join AC]

Question

Philoid · Accepted Answer

Given,

ABCD is a trapezium in which AB||DC.

Joining diagonal AC, which intersects EF at O.

In ΔADC, E is mid-point of AD and OE || CD.

By mid-point theorem, O is mid-point of AC.

Similarly,

In ΔCBA, O is mid-point of AC and OF||AB.

F is mid-point of BC by Mid-point Theorem.