About This Chapter
Who's it for?
Anyone who needs help understanding high school geometry material will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:
- Have fallen behind in understanding the postulates and principles of geometry.
- Need an efficient way to learn about the foundations of geometry.
- Learn best with engaging auditory and visual tools.
- Struggle with learning disabilities or learning differences, including autism and ADHD.
- Experience difficulty understanding your teachers.
- Missed class time and need to catch up.
- Can't access extra math learning resources at school.
How it works:
- Start at the beginning, or identify the topics that you need help with.
- Watch and learn from fun videos, reviewing as needed.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Submit questions to one of our instructors for personalized support if you need extra help.
- Verify you're ready by completing the Foundations of Geometry chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Foundations of Geometry chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- What is geometry?
- How are inductive and reductive methods of reasoning used in geometry?
- How did the ancient Greeks, Pythagoras and Thales, contribute to geometry?
- What is the axiomatic system, and how is it used?
- What geometric proofs originated with Euclid's postulates?
- Why are undefined terms important in geometry?
- What postulates and properties are associated with geometric figures?
- What algebraic laws also apply to geometry?
1. What is Geometry?
Geometry can be traced all the way back to 2000 BC. Watch this video lesson and learn how much geometry has grown over time, and how people from Egypt, Greece, and France have contributed to the geometry we now use today.
2. Inductive & Deductive Reasoning in Geometry: Definition & Uses
Watch this video lesson, and you will learn how important inductive and deductive reasoning is in the field of mathematics, especially when dealing with proofs in geometry. Learn how these two fundamental forms of reasoning give rise to formal theorems.
3. Thales & Pythagoras: Early Contributions to Geometry
In this video lesson, you will learn about the contributions Thales and Pythagoras made to the study of geometry. Also learn which of their major contributions is still in use today.
4. The Axiomatic System: Definition & Properties
Learn what kinds of things are included in an axiomatic system in this video lesson. Also learn why consistency, independence, and completeness are important in axiomatic systems.
5. Euclid's Axiomatic Geometry: Developments & Postulates
Learn how the way we do proofs in geometry had its start with Euclid in this video lesson. Learn about his contributions to the geometry we know today. Also learn about the five basic truths that he used as a basis for all other teachings.
6. Undefined Terms of Geometry: Concepts & Significance
What do points, lines, planes, and sets have in common? Watch this video lesson to find out what they are, what they look like, and why they are called undefined terms.
7. Properties and Postulates of Geometric Figures
In geometry, there are some basic postulates that are relied upon as the basis for other theorems. Watch this video to learn about the postulates that deal with points, lines, and planes.
8. Algebraic Laws and Geometric Postulates
Watch this video to learn about the basic algebraic laws that are also part of the basic geometric postulates that form the basis for the geometry that we know and study today.
9. Skew Lines in Geometry: Definition & Examples
In this lesson, learn the definition of skew lines. You will also learn tips for differentiating skew lines from parallel lines, as well as look at some examples.
10. What are Horizontal Lines? - Definition & Equations
In this lesson, we will learn about horizontal lines. What properties are unique to horizontal lines? How do you recognize the graph or equation of a horizontal line? These questions will be investigated here.
11. What are Parallel Lines? - Definition & Concept
In this lesson, you will learn about parallel lines and how you can identify and label them. You'll also find out how they are similar to things found in everyday life.
12. What is a Line Graph? - Definition & Examples
In this lesson, we'll explore the function and examples of a line graph. Then, you will learn to create questions and interpret data from line graphs. A brief quiz follows.
13. What is a Line Segment in Geometry? - Definition, Formula & Example
Line segments are essential elements to many geometric concepts. In this lesson you will explore line segments in geometry, learn the formula for finding the length of a line segment, review what you've learned with some examples, and test your understanding with a short quiz.
14. What is a Straight Line? - Definition & Examples
In this lesson, you will learn the definition and properties of a straight line. You will be given plenty of examples to ensure your understanding of straight lines. Following the lesson will be a brief quiz to test your new knowledge.
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Other chapters within the High School Geometry: Help and Review course
- Logic in Mathematics: Help and Review
- Introduction to Geometric Figures: Help and Review
- Properties of Triangles: Help and Review
- Triangles, Theorems and Proofs: Help and Review
- Parallel Lines and Polygons: Help and Review
- Similar Polygons: Help and Review
- Quadrilaterals: Help and Review
- Circular Arcs and Circles: Help and Review
- Conic Sections: Help and Review
- Geometric Solids: Help and Review
- Analytical Geometry: Help and Review
- Introduction to Trigonometry: Help and Review