In this chapter, you will explore the different relationships formed by parallel and perpendicular lines and planes. Different angle relationships will also be explored and what happens when lines are parallel. You will start to prove lines parallel or perpendicular using a fill-in-the-blank 2-column proof. There is also an algebra review of the equations of lines, slopes, and how that relates to parallel and perpendicular lines in geometry.
This chapter begins by comparing parallel and skew lines and presenting some of the basic properties of parallel lines. Perpendicular lines are then introduced and some basic properties and theorems related to perpendicular lines are explored. Building on the discussion of parallel lines, perpendicular lines, and transversals, the different angles formed when parallel lines are cut by a transversal are displayed. Corresponding angles, alternate interior angles, alternate exterior angles and their properties are presented. The algebra topics of equations of lines, slope, and distance are tied to the geometric concepts of parallel and perpendicular lines.