Question

PQRS is a trapezium in which PQ || SR and E is the midpoint of PS. If EG || PQ meets QR at G, show that G is the midpoint of QR

Answer 1

Construct a line to join diagonal QS

Diagonal QS intersect the line MN at point O

It is given that PQ∥SR and MN∥PQ

We can write it as

PQ∥MN∥SR

Consider △SPQ

We know that MO∥PQ and M is the midpoint to the side SP

O is the midpoint of the line QS

We know that MN∥SR

In △QRS we know that ON∥SR

O is the midpoint of the diagonal QS

Hence, based on the converse mid-point theorem we know that N is the midpoint of QR

therefore it is proved that N is the midpoint of QR