About This Chapter
Basics of Geometry - Chapter Summary
Feel confident that you fully grasp the basics of geometry by utilizing the helpful resources in this self-paced chapter. Watch fun online video lessons to study geometry concepts that include inductive reasoning, the axiomatic system and algebraic laws. Also, examine the history of geometry and learn about its early contributors. Test your understanding of the lessons you review by taking their accompanying multiple-choice quizzes. Use the practice exam to reinforce your knowledge of concepts covered in this chapter. When finished, you should be able to:
- Define geometry and discuss its beginnings in early Egypt and Greece
- Explain how inductive and deductive reasoning are used in geometry
- Share the early contributions Thales and Pythagoras made to the field of geometry
- Identify and discuss three properties of an axiomatic system
- Describe Euclid's early development of the axiomatic system
- List and discuss the undefined terms of geometry
- Provide the definitions of postulates and theorems and describe what they are used for
- Discuss the properties and postulates of geometric figures
- Understand the basics of various algebraic laws
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.
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Other chapters within the Geometry 101: Intro to Geometry course
- Logic & Proof in Mathematics
- Intro to Geometric Figures
- Triangle Properties & Construction
- Parallel Lines & Polygons
- Triangle Congruence
- Ratios & Proportions in Geometry
- Similar Polygons
- Quadrilaterals Overview
- Circles Overview
- Overview of Conic Sections
- 3D Geometry
- Analytical Geometry
- Non-Euclidean Geometry
- Introduction to Trigonometry
- Studying for Geometry 101