# Ch 2: Honors Geometry: Fundamentals of Geometry Proofs

### About This Chapter

## Honors Geometry: Fundamentals of Geometry Proofs - Chapter Summary and Learning Objectives

Here we provide text and video lessons to instruct you in the fundamentals of geometry proofs. Each lesson has a quiz to take at the end to assess your understanding of the material you just studied. If you need to restudy any part of a video lesson, either use the transcript or use the keyword-based timeline tool to go right to the section you need to replay. You can also ask a question of the instructor. When you have finished studying this chapter, you will be trained in:

- Euclid's axiomatic geometry
- Algebraic laws and geometric postulates
- Inductive and deductive reasoning in geometry
- Direct and indirect geometric proofs
- Converse of a statement
- Critical thinking and logic in mathematics

Lesson | Objective |
---|---|

Euclid's Axiomatic Geometry: Developments & Postulates | Learn the developments and postulates of Euclid's axiomatic geometry. |

Properties and Postulates of Geometric Figures | Discover the postulates of points, lines and planes. |

Algebraic Laws and Geometric Postulates | Analyze the basic algebraic laws and geometric postulates. |

Inductive & Deductive Reasoning in Geometry: Definition & Uses | Compare inductive and deductive reasoning and how they relate to geometry. |

Logical Equivalence: Converse, Inverse, Contrapositive & Counterexample | Get to know inverse, converse, contrapositive, counterexample and logical equivalence. |

Direct & Indirect Proof: Differences & Examples | Differentiate between direct and indirect proof. |

Geometric Proofs: Definition and Format | Get familiar with the parts that comprise geometric proofs. |

Converse of a Statement: Explanation and Example | Learn about the converse of a statement. |

Critical Thinking and Logic in Mathematics | Take a look at critical thinking and logic in mathematics. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. 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.

### 5. Logic Laws: Converse, Inverse, Contrapositive & Counterexample

Logical statements can be useful, but only if we are able to determine their validity. In this lesson, we'll look at the various forms of a logical statement and see how they relate to each other.

### 6. Direct & Indirect Proof: Differences & Examples

This lesson defines both direct and indirect proofs and, in turn, points out the differences between them. We'll also look at some examples of both types of proofs in both abstract and real-world contexts.

### 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.

### 8. Converse of a Statement: Explanation and Example

Just because a conditional statement is true, is the converse of the statement always going to be true? In this lesson, we'll learn the truth about the converse of statements.

### 9. Critical Thinking and Logic in Mathematics

Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.

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### Other Chapters

Other chapters within the Honors Geometry Textbook course

- Honors Geometry: Foundations of Geometry
- Honors Geometry: Logic in Mathematics
- Honors Geometry: Introduction to Geometric Figures
- Honors Geometry: Properties of Triangles
- Honors Geometry: Similar & Congruent Triangle Proofs
- Honors Geometry: Right Triangle Proofs
- Honors Geometry: Relationships Within Triangles
- Honors Geometry: Parallel Lines & Polygons
- Honors Geometry: Parallel Line Proofs
- Honors Geometry: Coordinate Geometry
- Honors Geometry: Analytical Geometry
- Honors Geometry: Similar Polygons
- Honors Geometry: Properties of Polygons & Circles
- Honors Geometry: Polygons & Quadrilaterals
- Honors Geometry: Circular Arcs & Circles
- Honors Geometry: Conic Sections
- High School Geometry: Geometric Solids
- Honors Geometry: Introduction to Trigonometry
- Honors Geometry: Right Triangles & Trigonometry
- Honors Geometry: Area, Surface Area & Volume
- Honors Geometry: Perimeter & Circumference
- Honors Geometry: Transformations
- Honors Geometry: Matrices