Question

ABCD is a trapezium in which AB || DC. BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F. Show that F is the mid-point of BC.

Answer 1

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

Let EF intersects BD at P. 

Then in ∆DAB 

Through E, EP || AB intersects BD at P. 

By the converse of mid-point theorem. 

=> P is the mid-point of BD.

Now in ∆BCD, P is the mid-point of BD. 

Through P, PF || DC intersects BC at P. 

By the converse of mid-point theorem. 

F is the mid-point of BC. 

Hence proved.