# Ch 3: Big Ideas Math Geometry Chapter 3: Parallel and Perpendicular Lines

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Parallel and Perpendicular Lines chapter of your textbook.
- Watch fun videos that cover the parallel and perpendicular line concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the geometry topics covered in the textbook chapter, including:

- What parallel, perpendicular and transverse lines are
- Proving a line is parallel
- How to use the perpendicular bisector theorem
- Finding and using slopes
- How to write a linear equation

*Big Ideas Math is a registered trademark of Larson Texts, Inc., which is not affiliated with Study.com.*

### 1. Parallel, Perpendicular and Transverse Lines

What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.

### 2. The Parallel & Perpendicular Postulates

Postulates are used in geometry to help prove theorems. This lesson explains how the parallel and perpendicular postulates will help to better understand the definition of parallel and perpendicular lines and how to prove theorems involving them.

### 3. Angles Formed by a Transversal

When you have a pair of parallel lines and a transversal, something very interesting happens to the angles that are formed. You can see this happen in real life at street intersections and such. Watch this video lesson to learn about all of this.

### 4. Parallel Lines: How to Prove Lines Are Parallel

Watch this video lesson to learn how you can prove that two lines are parallel just by matching up pairs of angles. Learn which angles to pair up and what to look for.

### 5. Using Converse Statements to Prove Lines Are Parallel

Because a pair of parallel lines produces unique angle characteristics, we can use this information to our advantage. Watch this video lesson to see how we turn this advantage into converse statements to help us prove parallel lines.

### 6. The Parallel Postulate: Definition & Examples

In this lesson, you will learn about an important postulate in Euclidean geometry, called the Parallel Postulate. It sounds kind of hard, but this lesson explains it in simple terms and provides several examples of it as well.

### 7. Constructing a Parallel Line Using a Point Not on the Given Line

Watch this video lesson, and you will learn how to draw parallel lines with just a compass and a straightedge. Also, learn why you would want to be able to do this in real life.

### 8. Transitive Property of Parallel Lines

The transitive property is one of the basic properties of mathematics that applies across different areas of mathematics from algebra to geometry. In this lesson you will see that it is a way to prove that multiple lines are parallel.

### 9. Perpendicular Bisector Theorem: Proof and Example

Perpendicular bisectors are multifunctional lines. They're not only perpendicular to the line in question, they also neatly divide it into two equal halves. In this lesson, we'll learn about the perpendicular bisector theorem.

### 10. Proving Theorems About Perpendicular Lines

In this lesson, you will be introduced to perpendicular lines, and the theorems related to them. You will also see the detailed proofs for these theorems

### 11. How to Find the Slope of a Perpendicular Line

In this lesson, we'll introduce the concept of slope and then discuss the relationship between the slopes of two perpendicular lines. Knowing this simple relationship will save you time on many math problems!

### 12. Using Slopes to Prove Lines Are Parallel or Perpendicular

This lesson will show us the relationship between slopes of parallel lines and the relationship between slopes of perpendicular lines. We will see how to use these relationships to prove that two lines are parallel or perpendicular.

### 13. How to Write a Linear Equation

Simply knowing how to take a linear equation and graph it is only half of the battle. You should also be able to come up with the equation if you're given the right information.

### 14. How to Find the Distance Between a Point & a Line

Finding the distance from a point to a line is useful in many science and engineering applications. In this lesson, we calculate this distance using a formula, as well as with some fundamental concepts from geometry and algebra.

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### Other Chapters

Other chapters within the Big Ideas Math Geometry: Online Textbook Help course

- Big Ideas Math Geometry Chapter 1: Basics of Geometry
- Big Ideas Math Geometry Chapter 2: Reasoning and Proofs
- Big Ideas Math Geometry Chapter 4: Transformations
- Big Ideas Math Geometry Chapter 5: Congruent Triangles
- Big Ideas Math Geometry Chapter 6: Relationships Within Triangles
- Big Ideas Math Geometry Chapter 7: Quadrilaterals and Other Polygons
- Big Ideas Math Geometry Chapter 8: Similarity
- Big Ideas Math Geometry Chapter 9: Right Triangles and Trigonometry
- Big Ideas Math Geometry Chapter 10: Circles
- Big Ideas Math Geometry Chapter 11: Circumference, Area, and Volume
- Big Ideas Math Geometry Chapter 12: Probability