Task# A Triangle's Interior Angles

Illustrative MathematicsVaries

This problem has students argue that the interior angles of the given triangle sum to 180 degrees, and then generalize to an arbitrary triangle via an informal argument. The completion of this task, together with the explanation of how it generalizes to any triangle constitutes an informal argument that the interior angles of any triangle add up to 180 degrees (a formal argument would involve proving from axioms and definitions that the pairs of angles used in the proof are alternate interior angles). The task gives students to demonstrate several Practice Standards.