In Fig. 6.20, DE || OQ and DF || OR. Show thatEF || QR.

 Given that In triangle POQ, DE parallel to OQ

Hence,

(Basic proportionality theorem)     (i)

Now,

                 In triangle POR, DF parallel OR

Hence,

(Basic proportionality theorem)     (ii)

From (i) and (ii), we get

Therefore,

EF is parallel to QR     (Converse of basic proportionality theorem)