document.write( "Question 1132255: Given: ABCD is a parallelogram with m < A = m < D. Prove: ABCD is a rectangle
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Algebra.Com's Answer #749227 by ikleyn(52798) $\"\"$ $\"About$

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document.write( "        Given: ABCD is a parallelogram with m (< A) = m (< D). Prove: ABCD is a rectangle.\r\n" );
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document.write( "In any parallelogram, the sum of the measures of two consecutive angles is equal to 180 degrees.\r\n" );
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document.write( "So, m (< A) + m(< D) = 180 degrees,    and\r\n" );
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document.write( "    m(< A) = M(< D).                   ( <<<---=== given ! )\r\n" );
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document.write( "Therefore,  m(< A) + m(< A) = 180 detrees,   or\r\n" );
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document.write( "            2m(< A) = 180 degrees, which implies  m(< A) = 90 degrees.\r\n" );
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document.write( "Thus in our parallelogram one angle is 90 degrees.\r\n" );
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document.write( "It means that EACH angle of the given parallelogram is 90 degrees, and hence the parallelogram is a rectangle.\r\n" );
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