Ch 21: FTCE Math: Foundations of Geometry

About This Chapter

Take an effective approach to studying for the FTCE Math exam by using our chapter. It will get you ready to answer questions that deal with the foundations of geometry.

FTCE Math: Foundations of Geometry - Chapter Summary

In order to review and remember important concepts and laws that pertain to geometry for the FTCE Math exam, look through each lesson in this chapter. They are designed to help you quickly cover topics that include:

  • Euclidean geometry
  • Euclid's axiomatic geometry
  • Deductive and inductive reasoning
  • The axiomatic system
  • Geometric figures and their properties and postulates
  • Algebraic laws and geometric proofs
  • Undefined terms of geometry

Acquire the right tactics for dealing with geometry-related material on this exam by utilizing our resources. Each one of our video lessons averages around 5-10 minutes in length, and they are designed to help you learn in an effective, fun manner. You might also want to use our self-assessment quizzes, as they can help you quickly assess how much material you picked up from this chapter.

8 Lessons in Chapter 21: FTCE 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 FTCE Mathematics 6-12 (026): Practice & Study Guide course

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