document.write( "Question 411688: What is the converse,inverse and contrapositive of this theorem?\r
\n" ); document.write( "\n" ); document.write( "The diagonals of a parallelogram bisect each other. \n" ); document.write( "
Algebra.Com's Answer #289337 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Original statement:\r\n" );
document.write( "The diagonals of a parallelogram bisect each other.\r\n" );
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document.write( "First re-write the original sentence using the words \"if\" and \"then\":\r\n" );
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document.write( "The original statement is talking about two line segments, so\r\n" );
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document.write( "Let p stand for \"two line segments are diagonals of a parallelogram\"\r\n" );
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document.write( "Let q stand for \"two line segments bisect each other\".\r\n" );
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document.write( "ORIGINAL STATEMENT REWRITTEN IN \"IF-THEN\" FORM:  p -> q\r\n" );
document.write( "If two line segments are diagonals of a parallelogram, then the two line\r\n" );
document.write( "segments bisect each other.\r\n" );
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document.write( "The clause between the \"if\" and the \"then\" is called the \"antecedent\".\r\n" );
document.write( "The clause following the \"then\" is called the \"consequence\".\r\n" );
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document.write( "In the above the clause p, or \"two line segments are diagonals of a\r\n" );
document.write( "parallelogram\" is the antecedent.\r\n" );
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document.write( "In the above the clause q, or \"two line segments bisect each other\" is the\r\n" );
document.write( "consequence.\r\n" );
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document.write( "THE CONVERSE: The converse swaps the antecedent and the consequence of the\r\n" );
document.write( "original statement:\r\n" );
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document.write( "q -> p\r\n" );
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document.write( "If two line segments bisect each other, then the two line segments are\r\n" );
document.write( "diagonals of a parallelogram.\r\n" );
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document.write( "THE INVERSE:  The inverse keeps antecedent and the consequence of the original\r\n" );
document.write( "statement but negates each:\r\n" );
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document.write( "~p -> ~q\r\n" );
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document.write( "If two line segments are NOT diagonals of a parallelogram, then the two line\r\n" );
document.write( "segments DO NOT bisect each other.\r\n" );
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document.write( "THE CONTRAPOSITIVE:  The Contrapositive does both of the above.  It swaps the\r\n" );
document.write( "antecedent and the consequence of the original statement and also negates them\r\n" );
document.write( "both.\r\n" );
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document.write( "~q -> ~p\r\n" );
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document.write( "If two line segments DO NOT bisect each other, then the two line segments are\r\n" );
document.write( "NOT diagonals of a parallelogram.\r\n" );
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document.write( "The original statement and the contrapositive are equivalent, that is,\r\n" );
document.write( "if one is true, so is the other, and if one is false, so is the other.\r\n" );
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document.write( "The inverse and the converse are also equivalent.\r\n" );
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document.write( "But the equivalent original statement and the contrapositive\r\n" );
document.write( "are not necessarily equivalent to the converse and the inverse. \r\n" );
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document.write( "Edwin
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