SOLUTION: Prove: the sum of the interior angles of a triangle is 180 degrees, can you please write a 2 column proof

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Question 173814: Prove: the sum of the interior angles of a triangle is 180 degrees, can you please write a 2 column proof
Answer by Edwin McCravy(6936) About Me  (Show Source):
You can put this solution on YOUR website!
Prove: the sum of the interior angles of a triangle is 180 degrees, can you please write a 2 column proof


Given: triangle ABC:

drawing%28400%2C170%2C-3%2C3%2C-1%2C2%2C+%0D%0Atriangle%28-1%2C0%2C2%2C0%2C0%2C1.5%29%2C%0D%0Alocate%28-1%2C0%2CA%29%2C%0D%0Alocate%282%2C0%2CC%29%2C%0D%0Alocate%280%2C1.8%2CB%29%0D%0A%0D%0A+%29



To prove:  ÐA + ÐB + ÐC = 180°

Draw line through B parallel to AC    Given a line and a pt. not on
and label two points D and E, one     the line, exactly one and only
on each side of B                     one line can be drawn thru
                                      the point parallel to the line.          
drawing%28400%2C170%2C-3%2C3%2C-1%2C2%2C+%0D%0Atriangle%28-1%2C0%2C2%2C0%2C0%2C1.5%29%2C%0D%0Alocate%28-1%2C0%2CA%29%2C%0D%0Alocate%282%2C0%2CC%29%2C%0D%0Alocate%280%2C1.8%2CB%29%2C%0D%0Aline%28-2%2C1.5%2C2%2C1.5%29%2Clocate%28-2%2C1.5%2CD%29%2Clocate%282%2C1.5%2CE%29%0D%0A+%29

ÐA = ÐABD                             Alternate interior angles formed by
                                      Transversal AB cutting parallel 
                                      lines AC and DE must be equal.

ÐC = ÐCBE                               alternate interior angles formed by
                                      Transversal CB cutting parallel 
                                      lines AC and DE must be equal.

ÐABD + ÐB + ÐCBE = 180°               Their sum is a straight angle.

ÐA + ÐB + ÐC = 180°                   Equals may be substituted for equals.

Edwin