document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100188>Question 1100188</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Triangle ABC is congruent to triangle DEF. Find the lengths of the given sides.<BR>\n" );
document.write( "BC= x+17<BR>\n" );
document.write( "EF= 4x+5\r<BR>\n" );
document.write( "\n" );
document.write( "So BC= ?<BR>\n" );
document.write( "and, EF= ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715718 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=715718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ABC is congruent with DEF means<BR>\n" );
document.write( "AB=DE , BC=EF , AC=DF , angle ABC=angle DEF, etc.<BR>\n" );
document.write( "As BC=EF , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B17=4x%2B5 ALIGN=MIDDLE  ALT=\"x%2B17=4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the equation they want you to write and solve.<BR>\n" );
document.write( "That is algebra coming to haunt students who thought it was safe to forget algebra while taking geometry.<BR>\n" );
document.write( "We solve equations by transforming them into easier ones.<BR>\n" );
document.write( "and we can always do that by adding the same expression to both sides of the equal sign,<BR>\n" );
document.write( "or by multiplying both sides of the equal sign times a nonzero real number:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=matrix%283%2C9%2C%0D%0A%22+%22%2Cx%2C%22%2B%22%2C17%2C%22=%22%2C%22+%22%2C4x%2C%22%2B%22%2C5%2C%0D%0A%22-%22%2Cx%2C%22-%22%2C5%2C%22=%22%2C%22-%22%2Cx%2C%22-%22%2C5%2C%0D%0A%22+%22%2C%22+%22%2C%22+%22%2C12%2C%22=%22%2C%22+%22%2C3x%2C%22+%22%2C%22+%22%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "After adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-5 ALIGN=MIDDLE  ALT=\"-x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=12 ALIGN=MIDDLE  ALT=\"3x=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and we can multiply both sides of the equal sign times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(We are allowed to call that dividing by 3, but see it as a multiplication)<BR>\n" );
document.write( "We get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%2F3=12%2F3 ALIGN=MIDDLE  ALT=\"3x%2F3=12%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=4%29 ALIGN=MIDDLE  ALT=\"highlight%28x=4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The teacher wants you to plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > in place of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in one of the expressions for the corresponding sides BC and EF.<BR>\n" );
document.write( "Or maybe the teacher wants yo to do that with both expressions and \"show your work.\"<BR>\n" );
document.write( " <BR>\n" );
document.write( "The expression for BC was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=x%2B17 ALIGN=MIDDLE  ALT=\"BC=x%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=4%2B17 ALIGN=MIDDLE  ALT=\"BC=4%2B17\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28BC=21%29 ALIGN=MIDDLE  ALT=\"highlight%28BC=21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "I am confident that I did not make any mistake solving the equation,<BR>\n" );
document.write( "and that EF=21 too, but maybe the teacher wants to see a verification.<BR>\n" );
document.write( "The expression for EF was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF=4x%2B5 ALIGN=MIDDLE  ALT=\"EF=4x%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF=4%2A4%2B5 ALIGN=MIDDLE  ALT=\"EF=4%2A4%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=EF=16%2B5 ALIGN=MIDDLE  ALT=\"EF=16%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28EF=21%29 ALIGN=MIDDLE  ALT=\"highlight%28EF=21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That proves that the length found for sides BC and EF<BR>\n" );
document.write( "(corresponding sides that should be congruent by CPCTC)<BR>\n" );
document.write( "are the same,strongly suggesting that the equation was set up correctly,<BR>\n" );
document.write( "and solved correctly.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Wordy explanation:<BR>\n" );
document.write( "When we say two triangles are congruent,<BR>\n" );
document.write( "we mean that they \"are twins\", that can be superimpose exactly,<BR>\n" );
document.write( "and we say the vertices' letters in such an order<BR>\n" );
document.write( "that the corresponding vertices are in the same place in the 3-letter sequence.<BR>\n" );
document.write( "That means that when we move and/or flip DEF,<BR>\n" );
document.write( "we can make A coincide with D,<BR>\n" );
document.write( "at the same time as B coincides with E,<BR>\n" );
document.write( "and C coincides with F.<BR>\n" );
document.write( "That tells us that the distance BC (from B to C) is the same as EF (from E to F).<BR>\n" );
document.write( "In geometry, we often invoke the fact that Corresponding Parts of Congruent Triangles are Congruent<BR>\n" );
document.write( "(abbreviated CPCTC).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );