Ch 26: TExES Physics/Math 7-12: Foundations of Geometry

About This Chapter

Before taking the TExES Physics/Mathematics 7-12 certification exam you will want to make sure you understand the foundations of geometry. Use this chapter to review the postulates and theorems of geometry, the axiomatic system and early contributions to geometry.

TExES Physics/Math 7-12: Foundations of Geometry - Chapter Summary

This chapter is composed of a series of lesson videos, worksheets and quizzes that review geometric reasoning, postulates and theorems. Watch these videos to improve your understanding of the axiomatic system and how algebraic laws are related to geometric postulates. After this series of lesson videos you should have a better understanding of:

  • Inductive and deductive reasoning in geometry
  • Contributions of Thales and Pythagoras
  • Properties of the axiomatic system and Euclid's axiomatic geometry
  • Significance and concept of undefined terms
  • Properties and postulates of geometric figures
  • Relationship between algebraic laws and geometry

Each lesson video is taught by professional instructors; if you come up with any questions during the duration of this chapter be sure to ask them for clarification. Also complete the lesson worksheets and quizzes to fully integrate the information presented in the lesson videos. Then, use your quiz results to find areas you didn't master and conquer them by returning to the lesson videos via video tags or reading over the lesson transcripts.

9 Lessons in Chapter 26: TExES Physics/Math 7-12: Foundations of Geometry
Test your knowledge with a 30-question chapter practice test
What is 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.

Inductive & Deductive Reasoning in Geometry: Definition & Uses

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.

Thales & Pythagoras: Early Contributions to Geometry

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.

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.

Euclid's Axiomatic Geometry: Developments & Postulates

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.

Undefined Terms of Geometry: Concepts & Significance

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.

Postulate in Math: Definition & Example

7. Postulate in Math: Definition & Example

In this lesson, we'll discuss the meaning of postulates in mathematics and explore some common examples. We'll also apply these postulates to solving some geometric problems.

Properties and Postulates of Geometric Figures

8. 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

9. 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.

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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