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

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3 years ago

Arun
25311 Points
```							ABCD be a parallelogram. To show that ABCD is a rectangle, we have to prove that one of its interior angles is 90º.In ΔABC and ΔDCB,AB = DC (Opposite sides of a parallelogram are equal)BC = BC (Common)AC = DB (Given)∴ ΔABC ≅ ΔDCB (By SSS Congruence rule)⇒ ∠ABC = ∠DCBIt is known that the sum of the measures of angles on the same side of transversal is 180º.∠ABC + ∠DCB = 180º (AB || CD)⇒ ∠ABC + ∠ABC = 180º⇒ 2∠ABC = 180º⇒ ∠ABC = 90ºSince ABCD is a parallelogram and one of its interior angles is 90º, ABCD is a rectangle
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3 years ago
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