Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Exercises from Illustrative Mathematics A set of exercises, commentary, and solutions. For this unit, choose:
G-CO Points equidistant from two points in the plane G-CO Congruent angles made by parallel lines and a transverse
Students know that corresponding angles, alternate interior angles, and alternate exterior angles of parallel lines are equal. Students know that when these pairs of angles are equal, then lines are parallel.
Students know that corresponding angles of parallel lines are equal because of properties related to translation. Students know that alternate interior angles of parallel lines are equal because of properties related to rotation.
Students present informal arguments to draw conclusions about angles formed when parallel lines are cut by a transversal.
Teacher and Student versions of full lesson from engageNY
What if you were presented with two angles that are on opposite sides of a transversal, but inside the lines? How would you describe these angles and what could you conclude about their measures? After completing this, you'll be able to answer these questions using your knowledge of alternate interior angles.
Lesson, videos, exercises, and text from CK-12. Additional resources available at this site.