Question

10. In a trapezium ABCD, AB || DC and point E is the mid - point of the side AD. A line through the point E and parallel to the side AB meets the line BC in F. Prove that F is the mid-point of BC.


is this solution correct ??

if one point is a mid point and is parallel to a side then the other point is also a mid point ​

Answer 1

Given: ABCD is a trapezium wherein AB || DC and Point E is the mid-point of the side AD.

To prove: F is the mid-point of BC

Proof:

Construction: Joing a diagonal AC which will intersect EF at a point O.

Proof: in ΔADC, E is the mid-point of AD and OE || CD. Thus, following the mid-point theorem, O would be the mid-point of AC.

Now, in ΔCBA, 0 is the mid-point of AC and OF || AB.

So, by mid-point theorem, F is the mid-point of BC.