document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197664>Question 1197664</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can you help me solve this problem? <BR>\n" );
document.write( "Given a quadrilateral whose vertices are ( 3, 5 ) , ( 4, -1 ), ( 8, -2 ) and ( 9, 7 ), show<BR>\n" );
document.write( "that the line segments joining the midpoints of adjacent sides from a parallelogram. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #831030 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=831030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Hi, can you help me solve this problem?<BR>\n" );
document.write( "Given a quadrilateral whose vertices are ( 3, 5 ) , ( 4, -1 ), ( 8, -2 ) and ( 9, 7 ), show<BR>\n" );
document.write( "that the line segments joining the midpoints of adjacent sides from a parallelogram.<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "This statement is true for ANY convex quadrilateral on a plane:\r\n" );
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document.write( "    for any convex quadrilateral on a plane, the segments joining\r\n" );
document.write( "    the midpoints of adjacent sides form a parallelogram.\r\n" );
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document.write( "The proof is in couple of lines.\r\n" );
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document.write( "    Draw one diagonal of the parallelogram.\r\n" );
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document.write( "    Then two of the four listed segments are midlines in the two triangles.\r\n" );
document.write( "    Therefore, these two segments are parallel to that diagonal and,\r\n" );
document.write( "    hence, are parallel to each other.\r\n" );
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document.write( "    Same reasoning works for other two segments and the other diagonal.\r\n" );
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document.write( "    Thus, these segments are in-pair parallel as opposite sides \r\n" );
document.write( "    of the drawn quadrilateral, proving that the drawn quadrilateral,\r\n" );
document.write( "    consisting of these segments is a parallelogram.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "The statement is proved and the proof is completed.\r<BR>\n" );
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document.write( "See the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/word/geometry/Midpoints-of-a-quadrilateral-are-vertices-of-the-parallelogram.lesson>Midpoints of a quadrilateral are vertices of the parallelogram</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook on Geometry\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;<A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "The referred lesson is the part of this online textbook under the topic &nbsp;\"<U>PROPERTIES OF PARALLELOGRAMS</U>\".\r<BR>\n" );
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document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in GEOMETRY<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson\r<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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