In this topic, you will study constructions involving angles and parallel lines using a compass and a straightedge. During your exploration, you will learn how to construct congruent angles. Congruent angles are angles that have the same measure. Also, you will explore how to construct parallel lines using your new knowledge of constructing congruent angles.

Essential Questions

• How are a compass and straightedge used to construct an angle bisector?
• How are a compass and straightedge used to construct an angle congruent to a given angle?
• How is a line parallel to given line that passes through a point not on the given line constructed using only a compass and a straightedge?

Warm-Up

Before you explore constructions involving angles and parallel lines, analyze the given diagram. Can you explain the relationship between lines n and m?