document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934565>Question 934565</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "ACDF and BCDE are parallelograms, segment AB is congruent to segment BE\r<BR>\n" );
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document.write( "Prove:<BR>\n" );
document.write( "ABEF is a rhombus </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568321 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=568321\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given that ACDF and BCDE are parallelograms.\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "AC = FD and AF = CD and CB = DE and CD = BE because opposite sides of parallelograms are congruent to each other.\r<BR>\n" );
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document.write( "since AF = CD and CD = BE, this means that AF = BE because of the transitive property that states that if a = b and b = c, then a = c.\r<BR>\n" );
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document.write( "you are given that AB congruent to BE.\r<BR>\n" );
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document.write( "AB is congruent to AC and CB by the partition postulate that states that the whole is equal to the sum of its parts.\r<BR>\n" );
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document.write( "this means that AC and CB are congruent to BE because of the transitive postulate that states if a = b and b = c, then a = c.   a in this case is AC + CB which is equal to AB which is equal to BE.\r<BR>\n" );
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document.write( "AC plus CB is congruent to FD + DE because of the addition postulate that states that if a = b and c = d, then a + c = b + d.\r<BR>\n" );
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document.write( "this also means that AB is congruent to FE because of the transitive property.\r<BR>\n" );
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document.write( "this also means that AB is congruent to FE is congruent to BE because of the transitive property again.\r<BR>\n" );
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document.write( "AF is congruent to BE as stated above because they are both congruent to CD and are therefore congruent to each other based on the transitive property that states that if a = b and b = c, then a = c.\r<BR>\n" );
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document.write( "you now have all 4 sides of the combined figure congruent to each other which is the basic definition of a rhombus.\r<BR>\n" );
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document.write( "all of the other properties of a rhombus can be proven from that.\r<BR>\n" );
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document.write( "here's a compilation of basic properties and postulates and theorems that you can reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://sites.google.com/site/johnnothdurft/salesianum-school/geometry-p-2/geometry-properties-theorems-postulates-etc\" target = \"_blank\">https://sites.google.com/site/johnnothdurft/salesianum-school/geometry-p-2/geometry-properties-theorems-postulates-etc</a>\r<BR>\n" );
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document.write( "i don't think the partition postulate is in there, but it is in other sources that i referenced.\r<BR>\n" );
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document.write( "while not an exact word for word proof, this should be sufficient for you to get a good idea of how to prove that ABEF is a thombus.\r<BR>\n" );
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document.write( "a picture of the rhombus is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/122401.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( " </SPAN>\n" );
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