document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205645>Question 1205645</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the value of x in the parallelogram when \r<BR>\n" );
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document.write( "DG = 4x, EF = 5x - 6, DE = 3x + 2, GF = 2x + 8\r<BR>\n" );
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document.write( "x = [x} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842579 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=842579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll assume the order of the points (either clockwise or counterclockwise) is D, E, F, G.\r<BR>\n" );
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document.write( "Perhaps your diagram looks something like this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C400%2C-5%2C5%2C-5%2C5%2C%0D%0Acircle%28-4%2C-2%2C0.05%29%2Ccircle%28-4%2C-2%2C0.07%29%2Ccircle%28-4%2C-2%2C0.09%29%2Ccircle%28-4%2C-2%2C0.11%29%2Ccircle%28-4%2C-2%2C0.13%29%2Ccircle%28-4%2C-2%2C0.15%29%2Ccircle%28-3%2C2%2C0.05%29%2Ccircle%28-3%2C2%2C0.07%29%2Ccircle%28-3%2C2%2C0.09%29%2Ccircle%28-3%2C2%2C0.11%29%2Ccircle%28-3%2C2%2C0.13%29%2Ccircle%28-3%2C2%2C0.15%29%2Ccircle%284%2C2%2C0.05%29%2Ccircle%284%2C2%2C0.07%29%2Ccircle%284%2C2%2C0.09%29%2Ccircle%284%2C2%2C0.11%29%2Ccircle%284%2C2%2C0.13%29%2Ccircle%284%2C2%2C0.15%29%2Ccircle%283%2C-2%2C0.05%29%2Ccircle%283%2C-2%2C0.07%29%2Ccircle%283%2C-2%2C0.09%29%2Ccircle%283%2C-2%2C0.11%29%2Ccircle%283%2C-2%2C0.13%29%2Ccircle%283%2C-2%2C0.15%29%2C%0D%0A%0D%0Aline%28-4%2C-2%2C-3%2C2%29%2Cline%28-3%2C2%2C4%2C2%29%2Cline%284%2C2%2C3%2C-2%29%2Cline%283%2C-2%2C-4%2C-2%29%2C%0D%0A%0D%0Aline%28-4.04%2C-0.18%2C-3.46%2C0.24%29%2Cline%28-3.46%2C0.24%2C-3.14%2C-0.26%29%2Cline%282.94%2C-0.14%2C3.54%2C0.22%29%2Cline%283.54%2C0.22%2C3.86%2C-0.28%29%2Cline%28-1.34%2C-1.5%2C-0.98%2C-1.96%29%2Cline%28-0.98%2C-1.96%2C-1.44%2C-2.44%29%2Cline%28-0.56%2C-1.5%2C-0.32%2C-1.96%29%2Cline%28-0.32%2C-1.96%2C-0.64%2C-2.46%29%2Cline%28-0.02%2C2.46%2C0.18%2C2%29%2Cline%280.18%2C2%2C-0.14%2C1.56%29%2Cline%280.98%2C2.44%2C1.18%2C2%29%2Cline%281.18%2C2%2C0.86%2C1.56%29%2C%0D%0A%0D%0Alocate%28-4.38%2C-2.16%2C%22D%22%29%2Clocate%28-3.26%2C2.38%2B0.2%2C%22E%22%29%2Clocate%283.96%2C2.36%2B0.2%2C%22F%22%29%2Clocate%283.1%2C-2.1%2C%22G%22%29%0D%0A%0D%0A%29%0D%0A%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If so, then DE is parallel and opposite FG. <BR>\n" );
document.write( "With any parallelogram, the opposite sides are congruent.<BR>\n" );
document.write( "DE = FG<BR>\n" );
document.write( "3x+2 = 2x+8<BR>\n" );
document.write( "3x-2x = 8-2<BR>\n" );
document.write( "x = 6\r<BR>\n" );
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document.write( "Also, opposite parallel sides EF and DG are congruent.<BR>\n" );
document.write( "EF = DG<BR>\n" );
document.write( "5x-6 = 4x <BR>\n" );
document.write( "5x-4x = 6<BR>\n" );
document.write( "x = 6\r<BR>\n" );
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document.write( "When x = 6, we have the following side lengths<BR>\n" );
document.write( "DE = 3x+2 = 3*6+2 = 20<BR>\n" );
document.write( "FG = 2x+8 = 2*6+8 = 20<BR>\n" );
document.write( "This confirms the 1st equation.<BR>\n" );
document.write( "EF = 5x-6 = 5*6-6 = 24<BR>\n" );
document.write( "DG = 4x = 4*6 = 24<BR>\n" );
document.write( "This confirms the 2nd equation.\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "DE = 20<BR>\n" );
document.write( "EF = 24<BR>\n" );
document.write( "FG = 20<BR>\n" );
document.write( "DG = 24<BR>\n" );
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