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. Show that F is the mid-point of BC.
Given ABCD is a trapezium in which AB ∥ CD and EF ∥ AB ∥ CD
Construction Join , the diagonal AC which intersect EF at O.
To show F is the mid-point of BC.Proof Now , in ΔADC, E is the mid-point of AD and OE ∥ CD
Thus, by mid-point theorem, O is mid-point of AC.
Now, in ΔCBA. O is the mid-point of AC and OF ∥AB.
So, by mid-point theorem, F is the mid-point of BC.