document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=389081>Question 389081</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given: A(2,3), B(5,-1), C(1,0), D(-4,-1), E(0,2), F(-1,-2)<BR>\n" );
document.write( "prove: angle ABC is congruent to angle DEF </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #275774 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=275774\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Instead of Pythagorean-theorem bashing, I'm only going to find the change in x and y for each pair of points:\r<BR>\n" );
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document.write( "(The partial differential operator <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta ALIGN=MIDDLE  ALT=\"delta\"   DISABLED_style= \"max-width:90%; height:auto;\" > should be uppercase, which represents a total change. Also, I'm taking the absolute value since Pythagorean theorem only depends on the squares of the numbers, regardless of whether change is positive or negative.\r<BR>\n" );
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document.write( "A,B<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28x%29+=+3 ALIGN=MIDDLE  ALT=\"delta%28x%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28y%29+=+4 ALIGN=MIDDLE  ALT=\"delta%28y%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "B,C<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28x%29+=+4 ALIGN=MIDDLE  ALT=\"delta%28x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28y%29+=+1 ALIGN=MIDDLE  ALT=\"delta%28y%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "C,A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28x%29+=+1 ALIGN=MIDDLE  ALT=\"delta%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28y%29+=+3 ALIGN=MIDDLE  ALT=\"delta%28y%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "D,E<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28x%29+=+4 ALIGN=MIDDLE  ALT=\"delta%28x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28y%29+=+3 ALIGN=MIDDLE  ALT=\"delta%28y%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "E,F<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28x%29+=+1 ALIGN=MIDDLE  ALT=\"delta%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28x%29+=+4 ALIGN=MIDDLE  ALT=\"delta%28x%29+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "D,F<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28x%29+=+3 ALIGN=MIDDLE  ALT=\"delta%28x%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%28x%29+=+1 ALIGN=MIDDLE  ALT=\"delta%28x%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We see that AB = DE = 5, AC = DF = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, BC = EF = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2817%29 ALIGN=MIDDLE  ALT=\"sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. By SSS, ABC and DEF are congruent triangles.<BR>\n" );
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