# Ch 9: Parallel Lines and Polygons

### About This Chapter

## Parallel Lines and Polygons - Chapter Summary and Learning Objectives

In this chapter, our instructors demonstrate several methods for determining whether two lines will intersect or remain the same distance apart. They also show you how to put these concepts to use in order to find measurements for a polygon's interior and exterior angles. Watch the short video lessons included here to learn about the following:

- Uses of the parallel postulate
- Angles created by transverses lines
- Properties and types of polygons
- Polygons' interior and exterior angles

Video | Objectives |
---|---|

The Parallel Postulate and Indirect Proof: Definition & Examples | Learn how the parallel postulate can be used to prove lines are parallel. |

Angles Formed by a Transversal | Explore the relationship between the angles created when a line transverses two parallel lines. |

Parallel Lines: How to Prove Lines Are Parallel | Use pairs of corresponding, alternate interior and alternate exterior angles created by a transversal to prove lines are parallel. |

Using Converse Statements to Prove Lines Are Parallel | Find out how converse statements about a transversal can be used to prove lines are parallel. |

What Are Polygons? - Definition and Examples | Examine the differences between regular, irregular, concave, convex, simple and complex polygons. |

Measuring the Area of Regular Polygons: Formula & Examples | Use a regular polygon's apothem and side lengths to calculate the area. |

Measuring the Angles of Triangles: 180 Degrees | Explain how parallel lines can be used to prove the sum of a triangle's interior angles. |

How to Measure the Angles of a Polygon & Find the Sum | Determine the measurements of a polygon's interior and exterior angles. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. What Are Polygons? - Definition and Examples

Watch this video lesson to see how the shapes that you grew up with are all related. Learn why the shapes of bricks, stars, and street blocks are considered polygons while the sun, moon, and rolling hills are not.

### 6. Regular Polygons: Definition & Parts

What makes a polygon a polygon? And what shapes are considered polygons? In this lesson, find out the answers to these questions and more as we learn all about polygons and their parts.

### 7. Measuring the Area of Regular Polygons: Formula & Examples

Watch this video lesson to learn why a regular polygon makes your life easier when it comes to finding the area inside one. Learn the one formula for area that will work for any type of regular polygon.

### 8. Measuring the Angles of Triangles: 180 Degrees

Watch this video lesson to see why a triangle's angles always add up to 180 degrees. Also, learn how you can use this unique fact about triangles to find an unknown angle in a triangle.

### 9. How to Measure the Angles of a Polygon & Find the Sum

Watch this video lesson to learn the one formula that lets you find the measure of angles in any regular polygon. Also, learn how you can tell if you are working with a regular polygon or not.

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### Other Chapters

Other chapters within the NY Regents Exam - Geometry: Test Prep & Practice course

- High School Geometry: Foundations of Geometry
- High School Geometry: Logic in Mathematics
- Introduction to Geometric Figures
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Analytical Geometry
- Triangles and Congruency
- Conic Sections
- Geometric Solids
- About the NY Regents Examinations
- NY Regents Exam - Geometry Flashcards