document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=347324>Question 347324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given XA=ZC Prove AC=ZX </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248580 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=248580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I assume by \"=\" you mean that the two expressions represent the same line segment.\r<BR>\n" );
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document.write( "If line segment XA = line segment ZC, then either:<BR>\n" );
document.write( "(1) X=Z, A=C, or<BR>\n" );
document.write( "(2) X=C, A=Z.\r<BR>\n" );
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document.write( "In either case the result follows by substitution. Q.E.D.\r<BR>\n" );
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document.write( "If by \"=\" you mean that two distinct line segments have the same length, then the claim is false. Here's a counterexample:<BR>\n" );
document.write( "X=(0,0)<BR>\n" );
document.write( "A=(1,1)<BR>\n" );
document.write( "C=(2,1)<BR>\n" );
document.write( "Z=(3,0)<BR>\n" );
document.write( "Then XA = ZC = &#8730;2, but <BR>\n" );
document.write( "1 = AC &#8800; ZX = 3.<BR>\n" );
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