document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003919>Question 1003919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If I knew that angle A and angle C were congruent. As well as angle B and angle D were congruent. How would I prove that ABCD is a parralelogram. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #620526 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53763)</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=620526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "If I knew that angle A and angle C were congruent. As well as angle B and angle D were congruent. How would I prove that ABCD is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28parallelogram%29 ALIGN=MIDDLE  ALT=\"highlight%28parallelogram%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "From the condition, &nbsp;you have &nbsp;&nbsp;<I>L</I><B>A</B> + <I>L</I><B>B</B> = <I>L</I><B>C</B> + <I>L</I><B>D</B>.\r<BR>\n" );
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document.write( "In addition, &nbsp;you know that the sum of internal angles of a quadrilateral is &nbsp;360°.\r<BR>\n" );
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document.write( "It implies that &nbsp;&nbsp;<I>L</I><B>A</B> + <I>L</I><B>B</B> = <I>L</I><B>C</B> + <I>L</I><B>D</B> = 180°.\r<BR>\n" );
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document.write( "In other words, the sum of two consecutive angles in your quadrilateral is 180° for any two consecutive angles.\r<BR>\n" );
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document.write( "It implies that your quadrilateral is a parallelogram. \r<BR>\n" );
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document.write( "(Because two consecutive angles are &nbsp;<U>interior angles at the same side</U>&nbsp; of two lines transversed by the third line. \r<BR>\n" );
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document.write( "Therefore, &nbsp;these two lines are parallel. &nbsp;See the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Angles/Parallel-lines.lesson>Parallel lines</A>&nbsp; in this site).\r<BR>\n" );
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