document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=696657>Question 696657</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i dont understand how to do a 2 column proof or what to write inside the 2 column proof. can you help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #429208 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=429208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A proof is just an orderly way to show that something is <BR>\n" );
document.write( "true, by building on other things <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=you+ ALIGN=MIDDLE  ALT=\"you+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=know ALIGN=MIDDLE  ALT=\"know\"   DISABLED_style= \"max-width:90%; height:auto;\" > are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=true ALIGN=MIDDLE  ALT=\"true\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "The only way that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=order ALIGN=MIDDLE  ALT=\"order\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+matters ALIGN=MIDDLE  ALT=\"+matters\"   DISABLED_style= \"max-width:90%; height:auto;\" > is that each thing you say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=must ALIGN=MIDDLE  ALT=\"must\"   DISABLED_style= \"max-width:90%; height:auto;\" > be based on something you've <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=already+ ALIGN=MIDDLE  ALT=\"already+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=said ALIGN=MIDDLE  ALT=\"said\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Often it will be based on the previous statement, <BR>\n" );
document.write( "but sometimes you will have to use earlier statements as well.\r<BR>\n" );
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document.write( " Your \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=givens ALIGN=MIDDLE  ALT=\"givens\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" are the foundation someone laid for you, and the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theorems ALIGN=MIDDLE  ALT=\"theorems\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=properties ALIGN=MIDDLE  ALT=\"properties\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=postulates ALIGN=MIDDLE  ALT=\"postulates\"   DISABLED_style= \"max-width:90%; height:auto;\" > you have to use to put together to a final goal, a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=proof ALIGN=MIDDLE  ALT=\"proof\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( ".Statements   ..........................          Reasons\r<BR>\n" );
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document.write( "    1. AB = CD   ......................          given<BR>\n" );
document.write( "    2. BC = BC  ......................           reflexive property<BR>\n" );
document.write( "    3. AB + BC = BC + CD ........  addition property of equality<BR>\n" );
document.write( "    4. A-B-C-D  ........................           given<BR>\n" );
document.write( "    5. AC = AB + BC  ................      definition of between<BR>\n" );
document.write( "    6. AC = BC + CD  ................      transitive property of equality<BR>\n" );
document.write( "    7. BC + CD = BD  .............      definition of between<BR>\n" );
document.write( "    8. AC = BD     .........       transitive property of equality\r<BR>\n" );
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document.write( "so, here is the foundation at the bottom  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=BD ALIGN=MIDDLE  ALT=\"AC=BD\"   DISABLED_style= \"max-width:90%; height:auto;\" >,and the goal at the top <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=CD ALIGN=MIDDLE  ALT=\"AB=CD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "statement 2 gives you a new fact you can build on that doesn't depend on <BR>\n" );
document.write( "the givens, but has been applied to a specific value, BC \r<BR>\n" );
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document.write( "statement 3 uses statements 1 and 2, by adding them together <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2BBC=BC%2BCD ALIGN=MIDDLE  ALT=\"AB%2BBC=BC%2BCD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "statement 4 is a given\r<BR>\n" );
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document.write( "statement 5 uses its definition \r<BR>\n" );
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document.write( "................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "...................|<BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%2BBC=BC%2BCD ALIGN=MIDDLE  ALT=\"AB%2BBC=BC%2BCD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " .....      / .......    \<BR>\n" );
document.write( " .......      2 .......    1\r<BR>\n" );
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document.write( ".....      / ..........    \<BR>\n" );
document.write( "   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+BC=BC ALIGN=MIDDLE  ALT=\"+BC=BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=CD ALIGN=MIDDLE  ALT=\"AB=CD\"   DISABLED_style= \"max-width:90%; height:auto;\" >    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+A-B-C-D ALIGN=MIDDLE  ALT=\"+A-B-C-D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC+=+AB+%2B+BC%7B%7B%7B%0D%0A%0D%0Astatement+6+combines+statements+3+and+5+using+transitivity+and+you+get+%7B%7B%7BAC+=+BC+%2B+CD ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "statement 7 is again based on the definition of between of statement 4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+%2B+CD+=+BD ALIGN=MIDDLE  ALT=\"BC+%2B+CD+=+BD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "finally we can join statements 6 and 7 to get to the goal which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC+=+BD ALIGN=MIDDLE  ALT=\"AC+=+BD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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