In Fig. 11.53, AB is the longest side and DC is the shortest side of a quadrilateral ABCD. Prove that ∠C > ∠A and ∠D> ∠B. [Hint

Question

In Fig. 11.53, AB is the longest side and DC is the shortest side of a quadrilateral
ABCD. Prove that ∠C > ∠A and ∠D> ∠B. [Hint : Join AC and BD].

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Kinsley 3 weeks 2021-09-07T04:02:43+00:00 1 Answer 0 views 0

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    2021-09-07T04:04:09+00:00

    Answer:Given:

    In quadrilateral ABCD, AB smallest & CD is longest sides.

    To Prove: ∠A>∠C

    & ∠B>∠D

    Construction: Join AC.

    Mark the angles as shown in the figure..

    Proof:

    In △ABC , AB is the shortest side.

    BC > AB

    ∠2>∠4 …(i)

    [Angle opposite to longer side is greater]

    In △ADC , CD is the longest side

    CD > AD

    ∠1>∠3 …(ii)

    [Angle opposite to longer side is greater]

    Adding (i) and (ii), we have

    ∠2+∠1>∠4+∠3

    ⇒∠A>∠C

    Similarly, by joining BD, we can prove that

    ∠B>∠D

    Please mark as the brainliest answer…………………………….

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