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

### About This Chapter

## 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.

### 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. 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.

### 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.

### 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.

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### Other Chapters

Other chapters within the TExES Physics/Mathematics 7-12 (243): Practice & Study Guide course

- TExES Physics/Math 7-12: Teaching Math & Science
- TExES Physics/Math 7-12: Basic Arithmetic
- TExES Physics/Math 7-12: Real Numbers
- TExES Physics/Math 7-12: Decimals & Fractions
- TExES Physics/Math 7-12: Ratios, Percent & Proportions
- TExES Physics/Math 7-12: Exponents & Exponential Expressions
- TExES Physics/Math 7-12: Algebraic Expressions & Equations
- TExES Physics/Math 7-12: Rational Expressions
- TExES Physics/Math 7-12: Radical Expressions
- TExES Physics/Math 7-12: Complex & Imaginary Numbers
- TExES Physics/Math 7-12: Number Theory
- TExES Physics/Math 7-12: Vector Operations
- TExES Physics/Math 7-12: Sequences & Series
- TExES Physics/Math 7-12: Functions
- TExES Physics/Math 7-12: Graphing & Functions
- TExES Physics/Math 7-12: Linear Equations
- TExES Physics/Math 7-12: Quadratic Equations
- TExES Physics/Math 7-12: Graphing & Factoring Quadratic Equations
- TExES Physics/Math 7-12: Matrices & Determinants
- TExES Physics/Math 7-12: Polynomials
- TExES Physics/Math 7-12: Exponential & Logarithmic Functions
- TExES Physics/Math 7-12: Trigonometry
- TExES Physics/Math 7-12: Continuity in Calculus
- TExES Physics/Math 7-12: Limits in Calculus
- TExES Physics/Math 7-12: Derivatives & Differentiation in Calculus
- TExES Physics/Math 7-12: Geometry and Measurement
- TExES Physics/Math 7-12: Geometric Figures
- TExES Physics/Math 7-12: Parallel Lines & Polygons
- TExES Physics/Math 7-12: Properties of Triangles
- TExES Physics/Math 7-12: Geometric Solids
- TExES Physics/Math 7-12: Analytical Geometry
- TExES Physics/Math 7-12: Similar Polygons
- TExES Physics/Math 7-12: Conic Sections
- TExES Physics/Math 7-12: Circular Arcs & Circles
- TExES Physics/Math 7-12: Triangle Theorems & Proofs
- TExES Physics/Math 7-12: Statistics
- TExES Physics/Math 7-12: Probability
- TExES Physics/Math 7-12: Discrete Probability Distributions
- TExES Physics/Math 7-12: Continuous Probability Distributions
- TExES Physics/Math 7-12: Statistical Inference
- TExES Physics/Math 7-12: Mathematical Reasoning
- TExES Physics/Math 7-12: Applied Math
- TExES Physics/Math 7-12: Scientific Inquiry & Process
- TExES Physics/Math 7-12: Vectors & Scalars
- TExES Physics/Math 7-12: Kinematics
- TExES Physics/Math 7-12: Motion
- TExES Physics/Math 7-12: Fluid Mechanics
- TExES Physics/Math 7-12: Linear Momentum
- TExES Physics/Math 7-12: Work, Energy & Power
- TExES Physics/Math 7-12: Laws of Gravitation
- TExES Physics/Math 7-12: Oscillations
- TExES Physics/Math 7-12: Rotational Motion & Conservation of Energy
- TExES Physics/Math 7-12: Heat & Energy
- TExES Physics/Math 7-12: Thermodynamics
- TExES Physics/Math 7-12: Electrical Forces & Fields
- TExES Physics/Math 7-12: Potential & Capacitance
- TExES Physics/Math 7-12: Current Circuits
- TExES Physics/Math 7-12: Magnetism
- TExES Physics/Math 7-12: Waves, Sound & Light
- TExES Physics/Math 7-12: Quantum Physics
- TExES Physics/Mathematics 7-12 Flashcards