in the given figure pqrs is a parallelogram . if A and B are points on QR and PS respectively such that QA=1/3 QR, SB=1/3SP. show that QASB is a parallelogram.

Dear Student,

Please find below the solution to the asked query :

We have, PQRS as the given parallelogram.Now, PQ = SR and PS = QR      Opposite sides of gm are equal   ....1and PQSR ; PSQR                  Opposite sides of gm are parallel    .....2Now, from 1, we have        PS = QRPS3 = QR3BS = QA               As it is given that BS = 13PS and QA = 13QRIn quadrilateral QASB,BS = QA    Proved aboveBS  QA     As, PSQRQASB is a gm    In a quadrilateral, if a pair of opposite sides is equal and , then quadrilateral is a gm

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