If the diagonals of a parallelogram are equal, then show that it is a rectangle. -Maths 9th

If the diagonals of a parallelogram are equal, then show that it is a rectangle. -Maths 9th
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Given : A parallelogram ABCD , in which AC = BD  TO Prove : ABCD  is a rectangle . Proof : In △ABC and △ABD AB = AB [common] AC = BD [given] BC = AD [opp . sides of a | | gm] ⇒ △ABC ≅ △BAD [ by SSS congruence axiom] ⇒ ∠ABC =  △BAD [c.p.c.t.] Also, ∠ABC + ∠BAD = 180° [co - interior angles] ⇒ ∠ABC + ∠ABC = 180° [∵ ∠ABC = ∠BAD] ⇒ 2∠ABC = 180°  ⇒ ∠ABC = 1 /2 × 180° = 90°  Hence, parallelogram ABCD is a rectangle.   
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Prove that the bisector of the angles of a parallelogram enclose a rectangle. -Maths 9th

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