Math, asked by kharedbela, 10 months ago

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.
pleaseee help me

Answers

Answered by amitnrw
4

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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