Question

E is the mid-point of the side AD of a trapezium ABCD in which AB || DC. Through E parallel to AB a line intersects BC at F. Show that F will be the mid-point of sides BC.

Answer 1

Given: ABCD is a trapezium in which AB || DC and E is mid-point of AD.

Construction: Draw EF || AB and join A to C.

To prove: F is mid-point of BC.

Proof: In ∆ADC, E is mid-point of AD and EO is drawn parallel to AB i.e., parallel to DC also. 

Then  by using converse of mid- point theorem, O will be the mid-point of AC.

Similarly, in ∆ABC, O is the mid-point of AC and OF || AB.

⇒ F will be the mid-point of BC.

(by converse of mid-point theorem)