**Theorem 6.3**: The
sizes of the
angles in a
triangle always add up
to* * 180^{o}.

**Proof**:

Behold!

Given* *triangle *ABC*,* *by Theorem
1.7, there is a line
through* **C *parallel to the
line determined by* **AB*.* *Since alternate interior angles are the
same size by
Theorem 6.1, we can conclude that the sum of
the sizes of
angles in the
triangle are equal to
the sum of the sizes of
the three angles meeting
at point* C *at the top of the
figure which can be seen to add up to a straight angle.