E is the mid-point of the side AD of the trapezium ABCD with `AB||DC`. A line through E drawn parallel to AB intersects BC at F. then

Options

A. Point F trisect BC
B. Point F bisect BC
C. AB=CD
D. None

Answer

B

Explanation

Given ABCD is a trapezium in which `AB||DC and EF||AB||CD`.
Construction Join, the diagonal AC which intersects EF at O.
To show F is the mid-point of BC.

Proof Now, in `Delta`ADC, E is the mid-point of AD and OE`||` CD.
Thus, by mid-point theorem, O is mid-point of AC.
Now, in `Delta`CBA, O is the mid-point of AC and OF `||` AB.
So, by mid-point theorem, F is the mid-point of BC.