. Grade 8, Illustrative icon
Task

Congruence of Alternate Interior Angles via Rotations

Illustrative MathematicsVaries

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.

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