Question

E is the mid-point of the side AD of the trapezium ABCD with AB || DC. A line through E drawn parallel to AB intersect BC at F. Show that F is the mid-point of BC. [Hint: Join AC]

Answer 1

Given: E is the mid-point of the side AD of the trapezium ABCD with AB || DC.

Also, EF || AB.

To prove: That F is the mid-point of BC.

Construction: Join AC which intersect EF at O.

Proof: In triangle ADC, E is the mid-point of AD and EF || DC.  ...[Since, EF || AB and DC || AB. So, AB || EF || DC]

O is the mid-point of AC and OF || AB.

Now, OF bisect BC.   ...[Converse of mid-point theorem]

Or F is the mid-point of BC.

Hence proved.