Question

Question 6
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.

Thinking process

Use the mid-point theorem, i.e the line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of it. Further show the required result.

Answer 1

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 $\Delta ADC$, 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.