Ch 27: CEOE Middle Level/Intermediate Math: Foundations of Geometry

About This Chapter

This chapter is preparatory for the Certification Examinations for Oklahoma Educators (CEOE) Middle Level/Intermediate Math test. The lessons in this chapter are on the foundations of geometry.

CEOE Middle Level/Intermediate Math: Foundations of Geometry - Chapter Summary

These lessons are to be used as a review for the CEOE Middle Level/Intermediate Math test. They will increase your competency for answering questions that could be included on the test about such things as:

  • The history and definition of Euclidean geometry
  • The developments and postulates of Euclid's axiomatic geometry
  • How to apply inductive and deductive reasoning in geometry
  • The definition and properties of the axiomatic system
  • Geometric figures' properties and postulates
  • Geometric postulates and algebraic laws
  • The definition and format of geometric proofs
  • The concepts and significance of geometry's undefined terms

Most of the lessons use a video format and are hosted by Study.com subject matter experts. Each is 5-10 minutes in length with a short quiz at the end to test your understanding. The text lesson spotlights key terms and words in bold type, letting you know what's important. There is also a quiz after the text lesson.

8 Lessons in Chapter 27: CEOE Middle Level/Intermediate Math: Foundations of Geometry
Test your knowledge with a 30-question chapter practice test
Euclidean Geometry: Definition, History & Examples

1. Euclidean Geometry: Definition, History & Examples

The lesson will explore the history and nature of Euclidean geometry, including its origins in Alexandria under Euclid and its five postulates. Its influence on the work of other mathematicians will also be covered.

Euclid's Axiomatic Geometry: Developments & Postulates

2. 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.

Inductive & Deductive Reasoning in Geometry: Definition & Uses

3. 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.

The Axiomatic System: Definition & Properties

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.

Properties and Postulates of Geometric Figures

5. 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.

Algebraic Laws and Geometric Postulates

6. 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.

Geometric Proofs: Definition and Format

7. Geometric Proofs: Definition and Format

Do you have something to prove? Can you explain why? In this lesson, we'll learn all about geometric proofs, including the parts that comprise a proof.

Undefined Terms of Geometry: Concepts & Significance

8. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the OSAT Middle Level/Intermediate Mathematics (CEOE) (125): Practice & Study Guide course

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