document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117575>Question 117575</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977274/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> How do you prove  the following theorem. <BR>\n" );
document.write( "If both pairs of an opposite sides of a quadrilateral are congruent, then the Quadrilateral is a paralleogram. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85616 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Theorem: If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.\r<BR>\n" );
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document.write( "Given: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=WZ ALIGN=MIDDLE  ALT=\"WZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > congruent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XY ALIGN=MIDDLE  ALT=\"XY\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=WX ALIGN=MIDDLE  ALT=\"WX\"   DISABLED_style= \"max-width:90%; height:auto;\" > congruent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ZY ALIGN=MIDDLE  ALT=\"ZY\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Prove: the quadrilateral <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+XYZW ALIGN=MIDDLE  ALT=\"+XYZW\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallelogram ALIGN=MIDDLE  ALT=\"parallelogram\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "proof:\r<BR>\n" );
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document.write( " let  angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ZX+W ALIGN=MIDDLE  ALT=\"ZX+W\"   DISABLED_style= \"max-width:90%; height:auto;\" > => angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, angle  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ZX+Y ALIGN=MIDDLE  ALT=\"ZX+Y\"   DISABLED_style= \"max-width:90%; height:auto;\" > => angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Y+Z+X ALIGN=MIDDLE  ALT=\"Y+Z+X\"   DISABLED_style= \"max-width:90%; height:auto;\" > => angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+Z+X ALIGN=MIDDLE  ALT=\"W+Z+X\"   DISABLED_style= \"max-width:90%; height:auto;\" > => angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Statements ALIGN=MIDDLE  ALT=\"Statements\"   DISABLED_style= \"max-width:90%; height:auto;\" >:	…………………………………………….............................<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Reasons ALIGN=MIDDLE  ALT=\"Reasons\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=WZ+ ALIGN=MIDDLE  ALT=\"WZ+\"   DISABLED_style= \"max-width:90%; height:auto;\" >congruent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XY ALIGN=MIDDLE  ALT=\"XY\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=WX ALIGN=MIDDLE  ALT=\"WX\"   DISABLED_style= \"max-width:90%; height:auto;\" > congruent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ZY ALIGN=MIDDLE  ALT=\"ZY\"   DISABLED_style= \"max-width:90%; height:auto;\" >………….... 1. Given\r<BR>\n" );
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document.write( "2. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XZ ALIGN=MIDDLE  ALT=\"XZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > congruent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XZ ALIGN=MIDDLE  ALT=\"XZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > ...............................................................2. Reflexive property\r<BR>\n" );
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document.write( "3. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DXYZ ALIGN=MIDDLE  ALT=\"DXYZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > congruent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DZWX ALIGN=MIDDLE  ALT=\"DZWX\"   DISABLED_style= \"max-width:90%; height:auto;\" >…………………............................... 3. SSS Postulate\r<BR>\n" );
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document.write( "4.<<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > congruent to <<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > congruent to <<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >………………….4. corresponding parts of congruent triangles are congruent\r<BR>\n" );
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document.write( "5. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=WZ ALIGN=MIDDLE  ALT=\"WZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > || <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XY ALIGN=MIDDLE  ALT=\"XY\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=WX+ ALIGN=MIDDLE  ALT=\"WX+\"   DISABLED_style= \"max-width:90%; height:auto;\" >||<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ZY+ ALIGN=MIDDLE  ALT=\"+ZY+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......................................................... 5. If two lines are cut by a transversal so that alternate interior angles  are congruent , the lines are ||.<BR>\n" );
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