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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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.