Congruence of Alternate Interior Angles via Rotations

This goal of this task is to experiment with rigid motions to help visualize why alternate interior angles (made by a transverse connecting two parallel lines) are congruent: this result can then be used to establish that the sum of the angles in a triangle is 180 degrees. Students will explore the impact of rotation by 180 degrees on lines in a carefully chosen setting. Teachers should expect informal arguments as students are only beginning to develop a formal understanding of parallel lines and rigid motions. This task provides a good opportunity to explore with geometry software (if available) or with physical manipulatives.