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Rajan@2021
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ABCD is a trapezium in which AB∣∣DC and its diagonals intersect each other at the point O. Show that AO/BO = CO/DO .

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In the given question we are asked to prove that AO/BO = CO/DO by using basic proportionality theorem, if ABCD is a trapezium in which AB∣∣DC and its diagonals intersect each other at the point O.

ML Aggarwal Avichal Publication class 10, Similarity, chapter 13.2, question no 8

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  1. Given parameters

    ABCD is a trapezium where AB || DC and diagonals AC and BD intersect at O.

    To prove

    AO/BO=CO/DO

    Construction

    Draw a line EF passing through O and also parallel to AB

    Now, AB ll CD

    By construction EF ll AB

    ∴ EF ll CD

    Consider the ΔADC,

    Where EO ll AB

    According to basic proportionality theorem

    AE/ED=AO/OC ……………………(1)

     

    Now consider Δ ABD

    where EO ll AB

    According to basic proportionality theorem

    AE/ED=BO/OD …………………..(2)

     

    From equation (1) and (2) we have

    AO/OC=BO/OD

    ⇒ AO/BO=OC/OD

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