ABCD is a parallelogram in which P and Q are midpoints of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, show

Question

ABCD is a parallelogram in which P and Q are midpoints of opposite sides AB and CD. If AQ intersects DP at S and BQ intersects CP at R, show that: (i) APCQ is a parallelogram. (ii) DPBQ is a parallelogram (iii) PSQR is a parallelogram

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Lydia 1 month 2021-08-14T15:08:00+00:00 2 Answers 0 views 0

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    0
    2021-08-14T15:09:31+00:00

    Answer:

    I think it helps you ⬇⬇

    Step-by-step explanation:

    (1)AB║CD and AB=DC

    ⇒AP║QC and 1/2AB=1/2DC

    ⇒AP║QC and AP=QC

    ∴APCQ is a parallelogram

    (2)AB║DC and AB=DC

    ⇒PB║DQ and 1/2AB=1/2DC

    ⇒PB║DQ and PB=DQ

    ∴DPBQ is a parallelogram

    (3)PC║AQ [∵APCQ is a parallelogram]

    ∴SO║PR

    and DP║QB [∵DPBQ is a parallelogram]

    ∴PS║QR

    ∴PSQR is a parallelogram

    ∴Hence proved

    0
    2021-08-14T15:09:43+00:00

    Answer:

    (i) APCQ is a parallelogram. (ii) DPBQ is a parallelogram (iii) PSQR is a parallelogram

    Step-by-step explanation:

    Given: ABCD is a parallelogram

    PQ=CQ=1/2DC

    AP=PB=1/2AB

    ∴AP=CQ=1/2AB

    AB||CD

    ∴AB||CQ  (AQCP)  Therefore, (i) APCQ is a parallelogram.

    simillarly,

    DP||BQ (DPBQ) Therefore,   (ii) DPBQ is a parallelogram.

    PS||QR (PSQR) Therefore, (iii)PSQR is a parallelogram

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