if a diagonals of parallelogram are equal then show it is a rectangle​

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if a diagonals of parallelogram are equal then show it is a rectangle​

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  1. Answer:

    □ ABCD is a parallelogram

    consider Δ ACD and Δ ABD

    AC = BD …. (given)

    AB = DC …. (opposite sides of parallelogram)

    AD = AD …. (common side)

    ∴Δ ACD ≅Δ ABD (sss test of congruence)

    ∠ BAD = ∠ CDA …. (cpct)

    ∠BAD+∠CDA=180

    ∘

    . [Adjacent angles of parallelogram are supplementary]

    so ∠ BAD and ∠ CDA are right angles as they are congruent and supplementary.

    Therefor, □ ABCD is a rectangle since a

    parallelogram with one right interior angle is a rectangle.

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