document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1134195>Question 1134195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> TriangleABC~DEF\r<BR>\n" );
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document.write( "If AB=3, DE=5, BC=9 find the length of EF. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #751486 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=751486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the triangles are similar, then the corresponding sides are proportional.\r<BR>\n" );
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document.write( "this means that the corresponding sides from one triangle to the other have the same ratio.\r<BR>\n" );
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document.write( "this means that AB / DE = BC / EF = AC / DF\r<BR>\n" );
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document.write( "AB / DE = 3 / 5\r<BR>\n" );
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document.write( "BC / EF = 9 / x\r<BR>\n" );
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document.write( "x is chosen as the value for the length of EF that you want to solve for.\r<BR>\n" );
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document.write( "since the ratios have to be the same, you have 3 / 5 = 9 / x\r<BR>\n" );
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document.write( "cross multiply to get 3 * x = 5 * 9\r<BR>\n" );
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document.write( "simplify to get 3 * x = 45\r<BR>\n" );
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document.write( "solve for x to get x = 45 / 3 = 15\r<BR>\n" );
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document.write( "your solution is that the length of EF is equal to 15.\r<BR>\n" );
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document.write( "you have AB / DE = BC / EF which results in 3 / 5 = 9 / 15.\r<BR>\n" );
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document.write( "cross multiply to get 3 * 15 = 5 * 9 which results in 45 = 45, confirming the ratios are the same.\r<BR>\n" );
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document.write( "note that the naming conventions for congruent or similar triangle require that the letters designating the triangle are present in the order of the corresponding sides and angle.\r<BR>\n" );
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document.write( "this means that, if triangle ABC is similar to triangle DEF, then:\r<BR>\n" );
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document.write( "the corresponding sides are AB to DE, BC to EF, AC to DF and the corresponding angles are A to D, B to E, C to F.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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