document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=233169>Question 233169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how do i prove<BR>\n" );
document.write( "if the diagnols of a parallelogram are congruent the parallelgram is a rectangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #172136 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=172136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If it is a parallelogram, then the opposite sides are equal.<BR>\n" );
document.write( "If the diagonals are also equal, then you have 4 congruent triangles.\r<BR>\n" );
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document.write( "to show you what i mean, let the parallelogram be PQRS.\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "PQ = SR\r<BR>\n" );
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document.write( "PS = QR\r<BR>\n" );
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document.write( "PR = SQ\r<BR>\n" );
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document.write( "you can break your parallelogram into 4 triangles.\r<BR>\n" );
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document.write( "those triangles are:\r<BR>\n" );
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document.write( "PRS and RPQ\r<BR>\n" );
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document.write( "SPQ and QRS\r<BR>\n" );
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document.write( "all these triangles are congruent by SSS as shown in the following diagram.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/090408.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "since all these triangles are congruent, then all their corresponding angles are congruent.\r<BR>\n" );
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document.write( "this means that angle PSR is congruent to angle RQP is congruent to angle  SPQ is congruent to angle QRS.\r<BR>\n" );
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document.write( "this means that all 4 angles of the parallelogram are congruent to each other.\r<BR>\n" );
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document.write( "this means that all the angles of the parallelogram are equal to 90 degrees.\r<BR>\n" );
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document.write( "since all the angles of a rectangle are equal to each other, this means that the parallelogram is a rectangle.\r<BR>\n" );
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document.write( "it hss all 4 angles equal to each other.<BR>\n" );
document.write( "it has both diagonals equal to each other.\r<BR>\n" );
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document.write( "that's all that you need because that's what defines a rectangle.\r<BR>\n" );
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document.write( "here's a definition of a rectangle from the web.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php\" target = \"_blank\">http://www.mathwarehouse.com/geometry/quadrilaterals/parallelograms/rectangle.php</a>\\r<BR>\n" );
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document.write( " </SPAN>\n" );
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