document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159549>Question 159549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Line AB is congruent to line CD, Line AB is parellel to line CD; prove that triangal ABD id congruent to triangle CDB\r<BR>\n" );
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document.write( "Help im so confused on what postulates and theorems i would use to prove this </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117667 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> use what you know to be true and work from there.<BR>\n" );
document.write( "problem states that AB congruent to CD.<BR>\n" );
document.write( "problem also states that AB parallel to CD.<BR>\n" );
document.write( "looks like you might have a parallelogram.<BR>\n" );
document.write( "draw AB above CD and parallel to it but not directly above it (a little to the left or a little to the right is ok).<BR>\n" );
document.write( "connect AC with a line, connect BD with a line, connect AD with a line.<BR>\n" );
document.write( "AB and CD are the given lines parallel to each other.<BR>\n" );
document.write( "AC and BD are additional lines you created to form at least a quadrilateral.<BR>\n" );
document.write( "AD is a diagonal from top left of the quadrilateral to bottom right of the quadrilateral.<BR>\n" );
document.write( "look at what you have and see what you can assume.<BR>\n" );
document.write( "you can assume that AB is congruent to CD because that is given.<BR>\n" );
document.write( "you can assume AD is congruent to AD because anything is equal to itself (reflexive property).<BR>\n" );
document.write( "you can assume that angle BAD is congruent to angle CDA because alternate interior angles of two parallel lines are equal.<BR>\n" );
document.write( "this is enough to prove that triangles ADC and triangles ABD are congruent to each other by SAS (side angle side).<BR>\n" );
document.write( "AB is congruent to CD (given)<BR>\n" );
document.write( "AD is congruent to AD (all things are equal to themselves)<BR>\n" );
document.write( "angle ADC congruent to angle BAD and is positioned between the other two congruent sides.<BR>\n" );
document.write( "i think that's your proof.<BR>\n" );
document.write( "1.  create AC, BD, and AD by construction (any two points make a line - i'm pretty sure you can assume these are postulates without having to prove them - you don't need to construct AB or CD because they were given)<BR>\n" );
document.write( "2.  prove diagonal AD is equal to itself (this would be a postulate - you don't have to prove it - it's called the reflexive property)<BR>\n" );
document.write( "3.  prove angle BAD congruent to angle ADC (alternate interior angles of parallel lines are congruent is a postulate of parallel lines).<BR>\n" );
document.write( "4.  triangles are congruent by SAS (also a postulate)<BR>\n" );
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document.write( "it looks like your proof depends on only postulates which were provided in your textbook.<BR>\n" );
document.write( "it does not depend on theorems that were proved earlier.<BR>\n" );
document.write( "if it did, you could state these theorems as proof in the same way you state postulates as proof.  they should not have to be proven again.<BR>\n" );
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document.write( "make sure you know your postulates as they are the building blocks for proving theorems and form the basis for what you can assume.<BR>\n" );
document.write( "make sure you know what theorems have been proven before since they are additional building blocks that you can use as you progress through the course.<BR>\n" );
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