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Prove that if opposite sides of any quadrilateral are equal then the quadrilateral will be a parallelogram​

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Prove that if opposite sides of any quadrilateral are equal then the quadrilateral will be a parallelogram​

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Harper

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2 thoughts on “<br /><br />Prove that if opposite sides of any quadrilateral are equal then the quadrilateral will be a parallelogram​”

  1. Answer:

    Given: Quadrilateral ABCD in which AB = DC and AD = BC$$

    To prove: ABCD is a parallelogram.

    Construction: Draw diagonal AC.

    Proof: Some statements and reasons for their validity are given below:

    Statement Reason

    AD=BC Given

    AB=CD Given

    AC=AC Common

    △CBA≅△ADC By SSS postulate

    ∠DCA=∠BAC Corresponding angles of congruent triangles

    DC∥AB Alternate angles are equal.

    ∠DAC=∠BCA Corresponding angles of congruent triangles

    AD∥BC Alternate angles are equal.

    It follows that ABCD is a parallelogram.

    Step-by-step explanation:

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