About This Chapter
How it works:
- Identify the lessons in Holt Geometry's Reasoning in Geometry chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the geometric reasoning topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Components of geometric proofs
- Reasoning and logic in mathematics
- The significance of undefined terms
- Geometric postulates and conjectures
- Properties of the axiomatic system
Holt Geometry is a registered trademark of Holt, Rinehart and Winston, which is not affiliated with Study.com.
1. 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.
2. 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.
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.
4. 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.
5. Types of Angles: Vertical, Corresponding, Alternate Interior & Others
In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements.
6. 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.
7. 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.
8. 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 within the Holt Geometry: Online Textbook Help course
- Holt Geometry Chapter 1: Exploring Geometry
- Holt Geometry Chapter 3: Parallels and Polygons
- Holt Geometry Chapter 4: Triangle Congruence
- Holt Geometry Chapter 5: Perimeter and Area
- Holt Geometry Chapter 6: Shapes in Space
- Holt Geometry Chapter 7: Surface Area and Volume
- Holt Geometry Chapter 8: Similar Shapes
- Holt Geometry Chapter 9: Circles
- Holt Geometry Chapter 10: Trigonometry
- Holt Geometry Chapter 12: A Closer Look at Proof and Logic