In XDE, PQ || DE……. Given
XP/PD = XQ/QE…….. (I) (Basic proportionality theorem)
In XEF, QR || EF……. Given
XR/RF = XQ/QE……. .(II) (Basic proportionality theorem)
XP/PD = XR/RF ………. from (I) and (II)
seg PR || seg DE ………. (converse of basic proportionality theorem)