Proof of Theorem 4.2.1

The sum of the interior angles of a triangle is 180°.

Consider the triangle below.
1. Construct a line through point A that is parallel to the base of the triangle.
2. Consider the segment connecting point A and angle β to be a transversal through two parallel lines. What do you know about the measure of the angle to the right of angle γ?
3. Consider the segment connecting point A and angle α to be a transversal through two parallel lines. What do you know about the measure of the angle to the left of angle γ?

Your knowledge of alternate interior angles allows you to discover that:
m<α + m<β + m<γ = ________°.

Kelly Shattuck, Created with GeoGebra