document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=556480>Question 556480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you set up an indirect proof & solve it? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #564407 by </B><A HREF=/tutors/aboutme.mpl?userid=EdenWolf><B>EdenWolf(517)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=EdenWolf><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=EdenWolf><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=564407\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <b>First, identify the conjecture to be proven. This is called the original conjecture. Let's say that the original conjecture is \"The sum of the measures of the angles of a triangle cannot be greater than 180 degrees.\" \r<BR>\n" );
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document.write( "Now, let's make an assumption, which is basically the opposite of the conjecture. For this example, the assumption will be: \"The sum of the measures of the angles of a triangle CAN be greater than 180 degrees.\"\r<BR>\n" );
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document.write( "Indirect proofs can be set up as two column proofs or as paragraph proofs. For this example, we will use a paragraph proof. </b>\r<BR>\n" );
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document.write( "Let's draw a triangle ABC first. <BR>\n" );
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document.write( "Draw a line ACD that cointains segment AC. This would actually be the first statement. The reason for that would be that through any two points, there is exactly one line. Each segment is contained on exactly one line.<BR>\n" );
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document.write( "Angle DCB is an exterior angle because of the definition of an exterior angle.\r<BR>\n" );
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document.write( "Angle DCB and angle ACB are a linear pair. Why? Because of the definition of a linear pair.\r<BR>\n" );
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document.write( "Now, the measure of angle DCB + the measure of angle ACB = 180 degrees by the Linear Pair Theorem.\r<BR>\n" );
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document.write( "The measure of angle ABC + the measure of angle CAB = the measure of angle DCB by the Exterior Angles Theorem.\r<BR>\n" );
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document.write( "Our last step: The measure of angle ABC + the measure of angle CAB + the measure of angle ACB = 180 degrees by substitution.\r<BR>\n" );
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document.write( "<b>Now we must write a contradiction: \"Therefore, the sum of the measures of angles of a triangle CANNOT be greater than 180 degrees.\" </b><BR>\n" );
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