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Ch 2: Honors Geometry: Fundamentals of Geometry Proofs

About This Chapter

The lessons in this chapter were developed to teach you about fundamentals of geometry proofs. We have incorporated several study tools to enhance your learning experience.

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.

9 Lessons in Chapter 2: Honors Geometry: Fundamentals of Geometry Proofs
Test your knowledge with a 30-question chapter practice test
Euclid's Axiomatic Geometry: Developments & Postulates

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.

Properties and Postulates of Geometric Figures

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.

Algebraic Laws and Geometric Postulates

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.

Inductive & Deductive Reasoning in Geometry: Definition & Uses

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.

Logic Laws: Converse, Inverse, Contrapositive & Counterexample

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.

Direct & Indirect Proof: Differences & Examples

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.

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.

Converse of a Statement: Explanation and Example

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.

Critical Thinking and Logic in Mathematics

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.

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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