document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210469>Question 1210469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which of the following conditions ensures that triangles ABC and DEF are similar?  Select all that apply.\r<BR>\n" );
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document.write( "(1) A = B, D = C, F = E, B = A, AB/AD = BC/BE\r<BR>\n" );
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document.write( "(2) A = D, AB/EF = BC/DE\r<BR>\n" );
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document.write( "(3) AB perp CD, DE perp AE, AB = DE and BC = BD\r<BR>\n" );
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document.write( "(4) AB parallel to BC, AB parallel to AC, CA parallel to FD </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852805 by </B><A HREF=/tutors/aboutme.mpl?userid=n2><B>n2(82)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=n2><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Which  of the following conditions ensures that triangles ABC and DEF are similar? Select all that apply.\r<BR>\n" );
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document.write( "(1) A = B, D = C, F = E, B = A, AB/AD = BC/BE<BR>\n" );
document.write( "(2) A = D, AB/EF = BC/DE<BR>\n" );
document.write( "(3) AB perp CD, DE perp AE, AB = DE and BC = BD<BR>\n" );
document.write( "(4) AB parallel to BC, AB parallel to AC, CA parallel to FD<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The analysis by &nbsp;@CPhill in part &nbsp;(2) &nbsp;is incorrect and his conclusion \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;for this part is incorrect, &nbsp;too.\r<BR>\n" );
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document.write( "Indeed,  one condition, A = D, does relate to angles A and D.\r\n" );
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document.write( "The second condition,  AB/EF = BC/DE,  can be equivalently rewritten in the form\r\n" );
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document.write( "    AB/BC = EF/DE,\r\n" );
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document.write( "and this form tells us that this proportion relates to the sides concluding angles\r\n" );
document.write( "B in triangle ABC and E in triangle DEF.\r\n" );
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document.write( "In any case, this proportion is not applicable to congruent angles A and D,\r\n" );
document.write( "so, WE CAN NOT CONCLUDE that triangles ABC and DEF are similar: we have no BASE\r\n" );
document.write( "to make such a conclusion.\r\n" );
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document.write( "So, again, in part (2), the analysis and the conclusion by @CPhill are incorrect.\r<BR>\n" );
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document.write( "My conclusion after consideration of solution by @CPhill is as follows:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(a) &nbsp;&nbsp;too many words and irrelevant reasoning that confuse the reader;\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(b) &nbsp;&nbsp;absence of the correct firm general idea/conception.\r<BR>\n" );
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document.write( "My evaluation of the work by @CPhill &nbsp;(same as his version of &nbsp;\" Artificial intelligence \")\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;in the scale &nbsp;\" acceptable - unacceptable \" :\r<BR>\n" );
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document.write( "<H3>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Unacceptable</H3><BR>\n" );
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document.write( " </SPAN>\n" );
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