Question 173814
Prove: the sum of the interior angles of a triangle is 180 degrees, can you please write a 2 column proof
<pre><font size = 4 color="indigo"><b>

Given: triangle ABC:

{{{drawing(400,170,-3,3,-1,2, 
triangle(-1,0,2,0,0,1.5),
locate(-1,0,A),
locate(2,0,C),
locate(0,1.8,B)

 )}}}



To prove:  <font face="symbol">Ð</font>A + <font face="symbol">Ð</font>B + <font face="symbol">Ð</font>C = 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(400,170,-3,3,-1,2, 
triangle(-1,0,2,0,0,1.5),
locate(-1,0,A),
locate(2,0,C),
locate(0,1.8,B),
line(-2,1.5,2,1.5),locate(-2,1.5,D),locate(2,1.5,E)
 )}}}

<font face="symbol">Ð</font>A = <font face="symbol">Ð</font>ABD                             Alternate interior angles formed by
                                      Transversal AB cutting parallel 
                                      lines AC and DE must be equal.

<font face="symbol">Ð</font>C = <font face="symbol">Ð</font>CBE                               alternate interior angles formed by
                                      Transversal CB cutting parallel 
                                      lines AC and DE must be equal.

<font face="symbol">Ð</font>ABD + <font face="symbol">Ð</font>B + <font face="symbol">Ð</font>CBE = 180°               Their sum is a straight angle.

<font face="symbol">Ð</font>A + <font face="symbol">Ð</font>B + <font face="symbol">Ð</font>C = 180°                   Equals may be substituted for equals.

Edwin</pre>