ABCD is a quadrilateral in which ab is equal to BC if P Q R S be the midpoint of Ab BC CD and BD respectively so that pqrs is a rh

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ABCD is a quadrilateral in which ab is equal to BC if P Q R S be the midpoint of Ab BC CD and BD respectively so that pqrs is a rhombus​

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Peyton 1 month 2021-08-06T06:57:44+00:00 1 Answers 0 views 0

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    2021-08-06T06:59:40+00:00

    In △BAD, P and S are mid-points of AB and BD

    ⇒ PS∥AD and PS=

    2

    1

    AD — ( 1 ) [ By BPT ]

    Similarly in △CAD,

    ⇒ OR∥AD and QR=

    2

    1

    AD — ( 2 )

    From ( 1 ) and ( 2 ), we get

    ⇒ PS∥QR and PS=QR=

    2

    1

    AD —— ( 3 )

    In △BDC, we get

    ⇒ SR∥BC and SR=

    2

    1

    BC —– ( 4)

    And in △ABC

    PQ∥BC and PQ=

    2

    1

    BC —— ( 5 )

    ⇒ PQ∥SR, PQ=SR=

    2

    1

    BC —- ( 6 ) [ From ( 4 ) and ( 5 ) ]

    ∴ □PQRS is a parallelogram.

    Now, AD=BC

    2

    1

    AD=

    2

    1

    BC

    ∴ PS=QR=PQ=SR [ From ( 3 ) and ( 6 ) ]

    ∴ □PQRS is a rhombus.

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