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(20055)   (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:





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.          


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
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