document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131983>Question 1131983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The coordinates of the vertices of parallelogram ABCD are A(&#8722;1, &#8722;3), B(7, 2), C(5, 8), and D(&#8722;3, 3). Using<BR>\n" );
document.write( "the diagonals, determine whether or not ABCD is a rhombus. Show all your work and state appropriate<BR>\n" );
document.write( "formulas and theorems used. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748753 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The rhombus has the following properties: All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary). All sides are congruent by definition. The diagonals bisect the angles.\r<BR>\n" );
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document.write( "let’s check if all four sides are congruent \r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=formula_distance.solver>Distance Between 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug in the numbers,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%287-%28-1%29%29%5E2%29%2B%28%282-%28-3%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%287-%28-1%29%29%5E2%29%2B%28%282-%28-3%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%5E2%2B5%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%288%5E2%2B5%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The distance is 9.4339811320566.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB=9.4339811320566 ALIGN=MIDDLE  ALT=\"AB=9.4339811320566\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=formula_distance.solver>Distance Between 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug in the numbers,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28-3-%285%29%29%5E2%29%2B%28%283-%288%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28-3-%285%29%29%5E2%29%2B%28%283-%288%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-8%5E2%2B-5%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28-8%5E2%2B-5%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The distance is 9.4339811320566.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD=+9.4339811320566 ALIGN=MIDDLE  ALT=\"CD=+9.4339811320566\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=formula_distance.solver>Distance Between 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug in the numbers,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%287-%285%29%29%5E2%29%2B%28%282-%288%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%287-%285%29%29%5E2%29%2B%28%282-%288%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%5E2%2B-6%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%282%5E2%2B-6%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The distance is 6.32455532033676.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC=6.32455532033676 ALIGN=MIDDLE  ALT=\"BC=6.32455532033676\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=formula_distance.solver>Distance Between 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance formula is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug in the numbers,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28%28-3-%28-1%29%29%5E2%29%2B%28%283-%28-3%29%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%28%28-3-%28-1%29%29%5E2%29%2B%28%283-%28-3%29%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-2%5E2%2B6%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28-2%5E2%2B6%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The distance is 6.32455532033676.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD=6.32455532033676 ALIGN=MIDDLE  ALT=\"AD=6.32455532033676\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since only opposite sides of a parallelogram are congruent, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABCD ALIGN=MIDDLE  ALT=\"ABCD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > a rhombus, it is a parallelogram\r<BR>\n" );
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