The purpose of this lesson is for students to connect rigid transformations with the congruence of angles created by a set of parallel lines cut by a transversal. They are also introduced to the terms complementary, for describing two angles whose measures add to , and supplementary, for describing two angles whose measures add to . 

Students identify angle measures on an image and describe what they notice about the angle measures using precise language (MP6). Then students use 180 degree rotations to explain why a pair of alternate interior angles are congruent (MP3). Students may connect these arguments to ones they made in a previous lesson when they justified that vertical angles are congruent. Finally, students use their arguments to generalize that for any pair of parallel lines cut by a transversal, the two pairs of alternate interior angles are congruent. 

In the optional activities, students have additional opportunities to find complementary, supplementary, and vertical angles and to further analyze their arguments about alternate interior angles. They find unknown angle measures and compare angles formed by parallel lines cut by a transversal to angles formed by a pair of non-parallel lines cut by a third line.

This lesson is the first time students see the terms “complementary” and “supplementary” angles in this course. Make sure to highlight the use of these terms during the Lesson Synthesis in addition to the focus on alternate interior angles. Here are some possible questions to include in the discussion:

• “What does it mean for two angles to be supplementary?” (Their measures sum to .)
• “What does it mean for two angles to be complementary?” (Their measures sum to .)
• “If you know two angles are supplementary and you know the measure of one angle, how can you find the other?” (Subtract the known one from .)