document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=937428>Question 937428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how to prove this theorem..\r<BR>\n" );
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document.write( "Theorem 7.5 If the diagonal of a quadrilateral bisect each other, the quadrilateral is 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 #570875 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=570875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> draw your quadrilateral ABCD so that A is top left, B is top right, C is bottom right, E is bottom left.\r<BR>\n" );
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document.write( "draw your diagonals AC and BD.\r<BR>\n" );
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document.write( "let the intersection of the diagonals be point E.\r<BR>\n" );
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document.write( "you are given that AE is congruent to EC and DE is congruent to EB.\r<BR>\n" );
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document.write( "angle AEB is congruent to angle CED by virtue of the fact that they are vertical angles and all vertical angles are congruent.\r<BR>\n" );
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document.write( "similarly, angle AED is congruent to angle CEB for the same reason.\r<BR>\n" );
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document.write( "you get triangle AEB is congruent to triangle CED and you get triangle AED is congruent to triangle CEB by the SAS postulate that says that triangle are congruent if 2 corresponding sides and the angle between them are congruent.\r<BR>\n" );
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document.write( "you then get that AB is congruent to DC and you get AD is congruent to BC because corresponding parts of congruent triangles are congruent.\r<BR>\n" );
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document.write( "you then get that quadrilateral ABCD is a parallelogram because a quadrilateral is a parallelogram if the opposite sides are congruent.\r<BR>\n" );
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document.write( "a picture of your quadrilateral is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/010901.jpg\" alt=\"$$$\" </> </SPAN>\n" );
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