document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033853>Question 1033853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove quadrilateral LOVE is a rhombus but not a square.\r<BR>\n" );
document.write( "\n" );
document.write( "L (2,2) O (-1,1) V (-2,-2) E (1,-1) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648545 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=648545\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Quadrilateral LOVE is a parallelogram, with sides LO and VE having slope 1/3 and sides OV and LE having slope 3.  <BR>\n" );
document.write( "Also, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%28OL%29+=+sqrt%2810%29+=+abs%28OV%29 ALIGN=MIDDLE  ALT=\"abs%28OL%29+=+sqrt%2810%29+=+abs%28OV%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > after using the distance formula.\r<BR>\n" );
document.write( "\n" );
document.write( "It is enough to show that one of the interior angles is not a right angle.\r<BR>\n" );
document.write( "\n" );
document.write( "Angle OVE <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta ALIGN=MIDDLE  ALT=\"theta\"   DISABLED_style= \"max-width:90%; height:auto;\" > is evaluated as follows:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tan%28theta%29+=+%28m%5BOV%5D+-+m%5BVE%5D%29%2F%281%2Bm%5BOV%5D%2Am%5BVE%5D%29+=+%283-1%2F3%29%2F%281%2B3%2A%281%2F3%29%29+=+%288%2F3%29%2F2+=+4%2F3 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=theta+=+tan%5E-1%284%2F3%29+%3C%3Epi%2F2 ALIGN=MIDDLE  ALT=\"theta+=+tan%5E-1%284%2F3%29+%3C%3Epi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore LOVE is a rhombus but not a square. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );