ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that perimeter of triangle PQR is double the perimeter of triangle ABC.

ABC is a triangle and through A, B, C lines are drawn parallel to BC,

1.	ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that perimeter of triangle PQR is double the perimeter of triangle ABC.
Answer» AB PARALLEL to Qp and BC parallel to RQ so ABCQ is a parellogram Similarly BCAR and ABPC are parellogramBC=AQ and BC =RAA is midpoint of QR Similarly B and C are midpoint of PR and PQ respectively AB=1/2 PQ ; BC =1/2 QR and CA=1/2 PRPQ=2AB ; QR=2BC ; PR=2CANow perimeter of triangle PQR=PQ + QR+ PR =2(AB+BC+CA) =2 the perimeter of triangle ABC

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ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that perimeter of triangle PQR is double the perimeter of triangle ABC. ​

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ABC is a triangle and through A, B, C lines are drawn parallel to BC, CA and AB respectively intersecting at P, Q and R. Prove that perimeter of triangle PQR is double the perimeter of triangle ABC.