document.write( "Question 1075106: How to prove if a parallelogram is a rectangle, then its diagonals are congruent, and in that case the diagonals bisect each other.
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Algebra.Com's Answer #689810 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "1. \"if a parallelogram is a rectangle, then its diagonals are congruent.\"\r
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document.write( "Let a parallelogram be a rectangle.\r\n" );
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document.write( "Consider its diagonals. Consider two triangles that have the diagonals as their sides.\r\n" );
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document.write( "Prove that the triangles are congruent.\r\n" );
document.write( "For it, use the fact that in any parallelogram the opposite sides are congruent;\r\n" );
document.write( "hence, the triangles have two pairs of congruent sides.\r\n" );
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document.write( "The angles between these sides are congruent, since each of these angles is the right angle.\r\n" );
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document.write( "All these argumemts combined together provide the proof.\r\n" );
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\n" ); document.write( "\n" ); document.write( "2. \"in that case the diagonals bisect each other. \"\r
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document.write( "Unfortunately, this statement is not formulated unambiguously . . .  \r\n" );
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document.write( "The words \"in this case\" remain an unanswered question: in which case?\r\n" );
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document.write( "The general relevant statement is:\r\n" );
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document.write( "     In any parallelogram, the diagonals bisect each other.\r\n" );
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document.write( "See the lesson\r\n" );
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document.write( "    - Properties of diagonals of parallelograms \r\n" );
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document.write( "in this site.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook on Geometry\r
\n" ); document.write( "\n" ); document.write( " GEOMETRY - YOUR ONLINE TEXTBOOK \r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this textbook under the topic Properties of parallelograms.\r
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\n" ); document.write( "\n" ); document.write( " H a p p y l e a r n i n g !\r
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