document.write( "Question 832709: (indirect proof) given line t cuts the lines a and b ∠1 ≅ <2
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Algebra.Com's Answer #502171 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You did not tell us which angles are ∠1 and ∠2.  So I'll guess\r\n" );
document.write( "they are alternate interior angles.  But whatever they are, the\r\n" );
document.write( "gist of the problem is similar.\r\n" );
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document.write( "Assume for contradiction that a and b are not parallel.\r\n" );
document.write( "Then if we extend them far enough, they will meet at some \r\n" );
document.write( "point P.\r\n" );
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document.write( "m∠1 = m∠2  because measure of congruent angles are equal.\r\n" );
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document.write( "m∠2 + m∠3 = 180° because they form a linear pair\r\n" );
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document.write( "m∠1 + m∠3 = 180°  substituting equals for equals\r\n" );
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document.write( "m∠P + (m∠1 + m∠3) = 180°  the measures of the three angles of a triangle\r\n" );
document.write( "                         have sum 180°\r\n" );
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document.write( "m∠P + 180° = 180°  substituting 180° for (m∠1 + m∠3), equals for equals.\r\n" );
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document.write( "m∠P = 0°  subtracting equals from equals (180°=180°)\r\n" );
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document.write( "A triangle cannot have an angle with 0 measure.\r\n" );
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document.write( "Therefore we have reached a contradiction to the assumption that a and b\r\n" );
document.write( "are not parallel.\r\n" );
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document.write( "Therefore the assumption is incorrect and therefore a∥b\r\n" );
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document.write( "Edwin
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