Question

Prove that a line passing through mid point of one non parallel side of a trapezium parallel to parallel sides bisects the other non parallel side

Answer 1

Given : ABCD is a trapezium. EF is parallel to DC. and it bisects one of the non parallel sides.

To prove : EF bisects either of the diagonals of the trapezium

Proof : let EF bisects AD, i.e. E is the mid-point of AD.

In triangle ADC,

E is the mid-point of AD and

EM || DC (because e.g. parallel dc)

from the converse of the mid point theorem: the straight line drawn through the mid-point of one side of a triangle parallel to another , bisects the third side.

=> M is the mid point of AC.

if EF bisects AD at E , it also bisects the diagonal AC.

similarly we can show that if EF bisects BD at F , it also bisects the diagonal BD.

hope this helps you.