document.write( "Question 1042358: I really need help with 2 proofs i would love if someone helped me. thanks!\r
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\n" ); document.write( "\n" ); document.write( "1. Given: AB ≅ AC
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Algebra.Com's Answer #657330 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "You write your own 2-column proof.  I'll give you an outline\r\n" );
document.write( "for it with all the reasons to put into your 2-column proof.\r\n" );
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document.write( "You use the facts that \r\n" );
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document.write( "1. the largest interior angle and side of a triangle\r\n" );
document.write( "are opposite each other.\r\n" );
document.write( "2. the middle side interior angle and side of a triangle\r\n" );
document.write( "are opposite each other.\r\n" );
document.write( "3. the smallest interior angle and side of a triangle\r\n" );
document.write( "are opposite each other.\r\n" );
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document.write( "ΔABC is isosceles because AB≅AC, ∠B≅∠ACB because they are base angles \r\n" );
document.write( "of isosceles ΔABC.  ∠ACB is acute because the base angles of an isosceles\r\n" );
document.write( "triangle are always acute. \r\n" );
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document.write( "∠ACD is obtuse because it is supplementary to acute ∠ACB.\r\n" );
document.write( "∠ACD is the largest angle in ΔACD because it is obtuse.\r\n" );
document.write( "AD is the longest side of ΔACD because it is opposite\r\n" );
document.write( "the largest ∠ACD.  AD is longer than AC, because AD is the \r\n" );
document.write( "longest side of ΔACD.  m(AD) > m(AB), because AB and AC have \r\n" );
document.write( "the same measure. m∠B > m∠D because in ΔABD, ∠B is opposite \r\n" );
document.write( "a longer side (AD) than the side ∠D is opposite (AB). \r\n" );
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\n" ); document.write( "2. Prove that there is no regular polygon with an interior angle
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document.write( "The sum of the interior angles of a polygon with n sides is given \r\n" );
document.write( "by the formula\r\n" );
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document.write( "Sum of interior angles = (n-2)*180°\r\n" );
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document.write( "A regular polygon of n sides has n congruent interior angles.\r\n" );
document.write( "So each interior angle of a regular polygon has measure\r\n" );
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document.write( "Assume for contradiction that there exists a polygon on n sides\r\n" );
document.write( "where n is a positive integer with an interior angle with measure \r\n" );
document.write( "145°.  Then \r\n" );
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document.write( ", where n is an integer.\r\n" );
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document.write( "Multiply both sides by n\r\n" );
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document.write( "Subtract 145°n from both sides\r\n" );
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document.write( "Add 360° to both sides\r\n" );
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document.write( "Divide both sides by 35°\r\n" );
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document.write( "That contradicts the assumption that n is a positive integer.  \r\n" );
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document.write( "Therefore there is no regular polygon with an interior angle \r\n" );
document.write( "whose measure is 145°.\r\n" );
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document.write( "Edwin

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