document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1018591>Question 1018591</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given: ad is perpendicular bisector of ce<BR>\n" );
document.write( " cd is congruent ae <BR>\n" );
document.write( "prove: cd is parallel ae </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635830 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let m be the midpoint of ad and ce.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=Parallel.png\">.<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=am=dm ALIGN=MIDDLE  ALT=\"am=dm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm=em ALIGN=MIDDLE  ALT=\"cm=em\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using the Pythagorean theorem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=am%5E2%2Bem%5E2=ae%5E2 ALIGN=MIDDLE  ALT=\"am%5E2%2Bem%5E2=ae%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2%2Bdm%5E2=cd%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2%2Bdm%5E2=cd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=em%5E2%2Bam%5E2=cd%5E2 ALIGN=MIDDLE  ALT=\"em%5E2%2Bam%5E2=cd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ae%5E2=cd%5E2 ALIGN=MIDDLE  ALT=\"ae%5E2=cd%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ae=cd ALIGN=MIDDLE  ALT=\"ae=cd\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
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document.write( "Look at the continuation of the red and black lines to the left of point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That angle H is equal to angle G because by trigonometry,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28H%29=em%2Fam ALIGN=MIDDLE  ALT=\"tan%28H%29=em%2Fam\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28G%29=cm%2Fdm ALIGN=MIDDLE  ALT=\"tan%28G%29=cm%2Fdm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28G%29=em%2Fam ALIGN=MIDDLE  ALT=\"tan%28G%29=em%2Fam\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28G%29=tan%28H%29 ALIGN=MIDDLE  ALT=\"tan%28G%29=tan%28H%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=G=H ALIGN=MIDDLE  ALT=\"G=H\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So when corresponding angles (G,H) are equal (from geometry), the lines are parallel.<BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ae ALIGN=MIDDLE  ALT=\"ae\"   DISABLED_style= \"max-width:90%; height:auto;\" > is parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cd ALIGN=MIDDLE  ALT=\"cd\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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