document.write( "Question 392003: 1.how to prove if the diagonals in a parallelogram are perpendicular, then the parallelogram is a rhombus.\r
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Algebra.Com's Answer #278192 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Outline for proof:\r\n" );
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document.write( "Since the diagonals of a parallelogram bisect each other,\r\n" );
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document.write( "BE and DE are congruent\r\n" );
document.write( "AE is congruent to itself\r\n" );
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document.write( "We are given that all four angles at point E are 90° and \r\n" );
document.write( "are therefore congruent.\r\n" );
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document.write( "Triangles ABE and ADE are congruent by side-angle-side, \r\n" );
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document.write( "Therefore AB and AD are congruent.\r\n" );
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document.write( "Since opposite sides of a parallelogram are congruent, \r\n" );
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document.write( "AD and BC are congruent, and  AB and CD are congruent.\r\n" );
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document.write( "So all four sides are congruent, so parallelogram ABCD\r\n" );
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document.write( "is a rhombus.\r\n" );
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document.write( "Outline:\r\n" );
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document.write( "We are given that diagonals AC and BD are congruent.\r\n" );
document.write( "AB and DC are congruent because they are opposite sides of a parallelogram\r\n" );
document.write( "AD is congruent to itself\r\n" );
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document.write( "Triangles ABD and DCA are congruent by side-side-side.\r\n" );
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document.write( "Angles BAD and CDA are congruent because they are corresponding\r\n" );
document.write( "angles of congruent triangles.\r\n" );
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document.write( "Angles BAD and CDA are also supplementary because \r\n" );
document.write( "angles of a parallelogram are supplementary.\r\n" );
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document.write( "Angles BAD and CDA are right angles because they are congruent\r\n" );
document.write( "and supplementary.  \r\n" );
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document.write( "Parallelogram ABCD is a rectangle because a parallelogram with one\r\n" );
document.write( "right interior angle is a rectangle.\r\n" );
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document.write( "Edwin
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