Question no. 15 From the side PQ of $△$PQR, cut off segment PL = QS. Draw LM$\parallel$QR and  ST$\parallel$PR. Show that MT$\parallel$PQ.

given,
LM ll QR
& ST ll PR
 
TO PROVE
MT ll PQ

          PL/ LQ = PM / MR            [ by BPT theorem as LM is parallel to QR]
        &QS/ PS=QT/TR                 [ by BPT theorem as ST is parallel to PR ]
 PL = SQ [ given]

and . PS = SL + PL

   PS = SL + SQ       [PL = SQ is given]
  PS =QL

PL/ QL=QT/TR  [ putting the value of SQ and PS ]
 
and ,
          PL/ LQ = PM / MR   
   therefore,
                   PM / MR  = QT/TR 

therefore , MT ll QR by the converse of midpoint theorem

I AM 100%  SURE OF MY ANSWER SO PLS THUMBS UP