document.write( "Question 831080: Proof a sum of of all angle of triangle is 180 \n" ); document.write( "
Algebra.Com's Answer #501123 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let's draw a triangle ABC:\r\n" );
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document.write( "Now through C, draw a line segment DE parallel to AC.\r\n" );
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document.write( "The two angles indicated by red arcs, ∠ACD and ∠BAC, are equal in measure \r\n" );
document.write( "because they are alternate interior angles when the transversal AC cuts\r\n" );
document.write( "the two parallel lines AB and DE.\r\n" );
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document.write( "Also the two angles indicated by green arcs, BCE and ABC, are equal in\r\n" );
document.write( "measure because they are alternate interior angles when the transversal\r\n" );
document.write( "BC cuts the two parallel lines AB and DE.\r\n" );
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document.write( "The sum of the measures of the three angles at the top have sum 180° \r\n" );
document.write( "because they form a straight angle. That is\r\n" );
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document.write( "m∠ACD + m∠ACB + m∠BCE = 180°  because they form straight angle ∠DCE\r\n" );
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document.write( "and since m∠ACD = m∠BAC, and  m∠BCE = m∠ABC, we can substitute\r\n" );
document.write( "equals for equals and get\r\n" );
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document.write( "m∠BAC + m∠ACB + m∠ABC = 180°.\r\n" );
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document.write( "That proves it.  But it's only an outline.  You should write it up in a \r\n" );
document.write( "two-column proof.\r\n" );
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document.write( "Edwin

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