document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=397983>Question 397983</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the midpoint quadrilateral theorem: the quadrilateral formed bt joining the midpoints of the consecutive sides of any quadrilateral is a parallelogram\r<BR>\n" );
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document.write( "how do i do the proof of the theorem?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #282073 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=282073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Analytic proof:<BR>\n" );
document.write( "Consider the quadrilateral WXYZ with the vertices  W (0,0), X (a,0), Y(b, c), and Z(d,e). The midpoint of side WX is (a/2, 0), while the midpoint of side XY is ((a+b)/2, c/2).  The slope of the line passing through these two midpoints is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%280-c%2F2%29%2F%28a%2F2-%28a%2Bb%29%2F2%29+=+%28-c%2F2%29%2F%28-b%2F2%29+=+c%2Fb ALIGN=MIDDLE  ALT=\"%0D%0A%280-c%2F2%29%2F%28a%2F2-%28a%2Bb%29%2F2%29+=+%28-c%2F2%29%2F%28-b%2F2%29+=+c%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The midpoint of side YZ is ((b+d)/2, (c+e)/2), while the midpoint of side ZW is (d/2, e/2).  The slope of the line passing through these two midpoints is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A%28%28c%2Be%29%2F2+-+e%2F2%29%2F%28%28b%2Bd%29%2F2+-+d%2F2%29+=+c%2Fb ALIGN=MIDDLE  ALT=\"%0D%0A%28%28c%2Be%29%2F2+-+e%2F2%29%2F%28%28b%2Bd%29%2F2+-+d%2F2%29+=+c%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  These two lines\sides would constitute one pair of parallel sides of the parallelogram.<BR>\n" );
document.write( "Now compute for the slope of the line connecting the midpoints of sides XY and YZ.<BR>\n" );
document.write( "Compute also for the slope of the line passing through the midpoints of ZW and WX.<BR>\n" );
document.write( "These two other sides would be the other pair of parallel sides of the parallelogram. </SPAN>\n" );
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