square abcd is a trapazeium in which ab||cd. P is the mid point of ad and pr||ab. prove that pr is half of (ab+cd)​

Question

square abcd is a trapazeium in which ab||cd. P is the mid point of ad and pr||ab. prove that pr is half of (ab+cd)​

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Aubrey 4 days 2021-09-14T11:54:52+00:00 1 Answer 0 views 0

Answers ( )

  1. Step-by-step explanation:

    ABCD is a trapezium and E,F are mid-points of diagonal AC and BD

    AB∥CD [ one par of opposite side is parallel in trapezium ]

    In △CDF and △GBF

    ⇒ DF=BF [ Since, F is mid-point of diagonal BD ]

    ⇒ ∠DCF=∠BGF [ DC∥GB and CG is a transversal ]

    ⇒ ∠CDF=∠GBF [ DC∥GB and BD is a transversal ]

    ∴ △CDF≅△GBF [ By ASA congruence rule ]

    ⇒ CD=GB [ C.P.C.T ] —- ( 1 )

    In △CAG, the points E and F are the mid-points of AC and CG respectively.

    ∴ EF=

    2

    1

    (AG)

    ⇒ EF=

    2

    1

    (AB−GB)

    From ( 1 )

    ⇒ EF=

    2

    1

    (AB−CD)

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