In a ΔABC, lines are drawn through A, B and C parallel to sides BC, CA and AB respectively forming a triangle PQR. Prove that BC = 
QR.
BC ïï RQ, AB ïï QP and AC ïï RP
To Prove: BC =
QR
Proof: Since QC ïï AB and QA ïï BC
... ABCQ is a parallelogram (opposite sides are parallel)
... BC = AQ ...... (opposite sides of parallelogram)....(i)
Similarly BCAR is a parallelogram and BC = AR ............(ii)
By adding (i) and (ii)
we get
2BC = AQ + AR = QR
... BC = QR.
To Prove: BC =
QRProof: Since QC ïï AB and QA ïï BC
... ABCQ is a parallelogram (opposite sides are parallel)
... BC = AQ ...... (opposite sides of parallelogram)....(i)
Similarly BCAR is a parallelogram and BC = AR ............(ii)
By adding (i) and (ii)
we get
2BC = AQ + AR = QR
... BC =
QR. 3