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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. Q.9

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The chapter from triangles how i solve the problem from exercise 6.2 of math subject, how i solve this problem in easy way 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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  1. Given, ABCD is a trapezium where AB || DC and diagonals AC and BD intersect each other at O.

    Ncert solutions class 10 chapter 6-12

    We have to prove, AO/BO = CO/DO

    From the point O, draw a line EO touching AD at E, in such a way that,

    EO || DC || AB

    In ΔADC, we have OE || DC

    Therefore, By using Basic Proportionality Theorem

    AE/ED = AO/CO ……………..(i)

    Now, In ΔABD, OE || AB

    Therefore, By using Basic Proportionality Theorem

    DE/EA = DO/BO…………….(ii)

    From equation (i) and (ii), we get,

    AO/CO = BO/DO

    ⇒AO/BO = CO/DO

    Hence, proved.

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