If the diagonal of parallogram are equal ,then show that it is rect.

1.	If the diagonal of parallogram are equal ,then show that it is rect.
Answer» Given : A parallelogram ABCD , in which AC = BD\xa0TO Prove :\xa0ABCD is a rectangle .Proof : In\xa0△ABC and\xa0△ABDAB = AB [common]AC = BD [given]BC = AD [opp . sides of a\xa0\| \| gm]⇒\xa0△ABC\xa0≅\xa0△BAD [ by SSS congruence axiom]⇒\xa0∠ABC =\xa0△BAD\xa0[c.p.c.t.]Also,\xa0∠ABC +\xa0∠BAD = 180° [co - interior angles]⇒\xa0∠ABC +\xa0∠ABC\xa0= 180°\xa0[∵\xa0∠ABC =\xa0∠BAD]⇒ 2∠ABC =\xa0180°\xa0⇒\xa0∠ABC = 1 /2\xa0×\xa0180° = 90°\xa0Hence, parallelogram ABCD is a rectangle.

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