in an isosceles trapezium mnop, mq and nr are perpendiculars to to po. show that triangle pqm= triangle orn and triangle pnr= tr

Question

in an isosceles trapezium mnop, mq and nr are perpendiculars to to po. show that triangle pqm= triangle orn and triangle pnr= triangle omq​

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Bella 2 weeks 2021-09-04T03:13:14+00:00 1 Answer 0 views 0

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    2021-09-04T03:14:29+00:00

    Answer:

    Area of  Δ PQM = Area of Δ ORN , ∠PNR = ∠OMQ

    Step-by-step explanation:

    In an isosceles trapezium MNOP, MQ and NR are perpendiculars to PO.

    MQ = NR  ( Perpendicular distance between parallel lines)

    PM = ON  ( Isosceles trapezium)

    ∠PQM = ∠ORN = 90°

    => PQ = OR  

    Area of  Δ PQM = (1/2) PQ * QM

    Area of Δ ORN = (1/2) OR * RN

    PQ = OR  *  QM = RN

    => Area of  Δ PQM = Area of Δ ORN

    in Δ PNR  & ΔOMQ

    RN = QM

    PR = OQ   (PR = PQ + QR   = OR + QR = OQ)

    ∠PRN = ∠OQM = 90°

    => Δ PNR ≅ ΔOMQ

    => ∠PNR = ∠OMQ

    QED

    Proved

    Step-by-step explanation:

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