Question

If the diagonals of parallelogram are equal, then show that it is a rectangle.​

Answer 1

Answer:

Ref.Image

□ 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.

Answer 2

$\bf \huge {\underline {\underline \red{AnSwEr}}}$

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Given

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• ABCD is a parallelogram.

• AB = CD, BC = AD and AC = BD

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To Prove

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• ABCD is a rectangle

• AB = CD, AC = BD

• ∠A = ∠B = ∠C = ∠D = 90°

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Proof

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ABCD is a parallelogram

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In Δ ACD and Δ ABD

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AC = BD [ given ]

AB = DC [ opposite sides of parallelogram ]

AD = AD [ common side ]

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∴Δ ACD ≅Δ ABD [ by SSS congruence ]

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∠ BAD = ∠ CDA [ by CPCT ]

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∠BAD+∠CDA=180 [Adjacent angles of parallelogram are supplementary]

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

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Therefore, ABCD is a rectangle since a

parallelogram with one right interior angle is a rectangle.