About This Chapter
Honors Geometry: Parallel Line Proofs - Chapter Summary and Learning Objectives
Parallel lines can be seen everywhere around us, from the lines marking traffic to artistic patterns, but what proof is there that these lines are truly parallel? In this chapter you will discover the proofs used to establish whether two lines are mathematically parallel to one another. Video lessons within the chapter allow you to see parallel line proofs in action. The quizzes available at the end of each lesson can help you gauge whether you have understood the materials. Topics covered in this chapter include:
- The angles of parallel lines
- The characteristics of parallel lines
- Proofs and indirect proofs
- The Parallel Postulate
- Transverse, perpendicular, and parallel lines
|Angles Formed by a Transversal||Examine parallel lines and identify the angles that occur when a transversal is introduced.|
|Parallel Lines: How to Prove Lines Are Parallel||Uncover the truth about angles that prove whether lines are parallel.|
|Using Converse Statements to Prove Lines Are Parallel||Learn how to construct converse statements and create mathematical proofs about parallel lines.|
|The Parallel Postulate and Indirect Proof: Definition & Examples||Define an indirect proof and indicate how the Parallel Postulate can be used in regards to parallel line proofs.|
|Parallel, Perpendicular and Transverse Lines||Go over the characteristics of each type of line and provide real-world examples.|
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
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Other chapters within the Honors Geometry Textbook course
- Honors Geometry: Foundations of Geometry
- Honors Geometry: Fundamentals of Geometry Proofs
- Honors Geometry: Logic in Mathematics
- Honors Geometry: Introduction to Geometric Figures
- Honors Geometry: Properties of Triangles
- Honors Geometry: Similar & Congruent Triangle Proofs
- Honors Geometry: Right Triangle Proofs
- Honors Geometry: Relationships Within Triangles
- Honors Geometry: Parallel Lines & Polygons
- Honors Geometry: Coordinate Geometry
- Honors Geometry: Analytical Geometry
- Honors Geometry: Similar Polygons
- Honors Geometry: Properties of Polygons & Circles
- Honors Geometry: Polygons & Quadrilaterals
- Honors Geometry: Circular Arcs & Circles
- Honors Geometry: Conic Sections
- High School Geometry: Geometric Solids
- Honors Geometry: Introduction to Trigonometry
- Honors Geometry: Right Triangles & Trigonometry
- Honors Geometry: Area, Surface Area & Volume
- Honors Geometry: Perimeter & Circumference
- Honors Geometry: Transformations
- Honors Geometry: Matrices