# Chapter 3: Parallel and Perpendicular Lines

**At Grade**Created by: CK-12

## Introduction

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 to these angles when lines are parallel. You will continue to use proofs, to prove that lines are parallel or perpendicular. There will also be a review of equations of lines and slopes and how we show algebraically that lines are parallel and perpendicular.

- 3.1.
## Parallel and Skew Lines

- 3.2.
## Perpendicular Lines

- 3.3.
## Corresponding Angles

- 3.4.
## Alternate Interior Angles

- 3.5.
## Alternate Exterior Angles

- 3.6.
## Same Side Interior Angles

- 3.7.
## Slope in the Coordinate Plane

- 3.8.
## Parallel Lines in the Coordinate Plane

- 3.9.
## Perpendicular Lines in the Coordinate Plane

- 3.10.
## Distance Formula in the Coordinate Plane

- 3.11.
## Distance Between Parallel Lines

### Chapter Summary

## Summary

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.

### Chapter Keywords

- Parallel
- Skew Lines
- Parallel Postulate
- Perpendicular Line Postulate
- Transversal
- Corresponding Angles
- Alternate Interior Angles
- Alternate Exterior Angles
- Same Side Interior Angles
- Corresponding Angles Postulate
- Alternate Interior Angles Theorem
- Alternate Exterior Angles Theorem
- Same Side Interior Angles Theorem
- Converse of Corresponding Angles Postulate
- Converse of Alternate Interior Angles Theorem
- Converse of the Alternate Exterior Angles Theorem
- Converse of the Same Side Interior Angles Theorem
- Parallel Lines Property
- Theorem 3-1
- Theorem 3-2
- Distance Formula: \begin{align*}d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\end{align*}
d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√

### Chapter Review

Find the value of each of the numbered angles below.

### Texas Instruments Resources

*In the CK-12 Texas Instruments Geometry FlexBook, there are graphing calculator activities designed to supplement the objectives for some of the lessons in this chapter. See http://www.ck12.org/flexr/chapter/9688.*