PQRS is a parallelogram and O is a point on SQ. there produced line PQ meets QR at T and SR produced at U. if SO = 3OQ then find the value of PQ/RU.
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PQ/RU = 1/2 PQRS is a parallelogram and O is a point on SQ. there produced line PO meets QR at T and SR produced at U. SO = 3OQ
Step-by-step explanation:
in Δ SOP & Δ QOT
∠SOP = ∠QOT ( opposite angles)
∠PSO = ∠TQO ( as PS ║ QT because PS ║ QR and T lies on QR )
=> Δ SOP ≈ Δ QOT
=> SO/QO = SP/QT
=> 3QO/QO = QR/QT (SP = QR opposite sides of parallelogram)
=> QR/QT = 3
=> (QT + TR)/QT = 3
=> 1 + TR / QT = 3
=> TR/QT = 2
=> QT/TR = 1/2
in Δ PTQ & ΔUTR
∠PTQ = ∠UTR
∠QPT = ∠RUT ( as PQ ║ RU because PQ ║ SR & RU is extension of SR)
=> Δ PTQ ≈ ΔUTR
=> QT/TR = PQ/RU
=> 1/2 = PQ/RU
PQ/RU = 1/2
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