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
Geometric proofs are the demonstration of a mathematical statement, true or false, using logic to arrive at a conclusion. See the components of proofs and how they are formatted through a sample problem provided in this lesson.
2. Critical Thinking and Logic in Mathematics
Mathematics involves logic and critical thinking to make connections and draw conclusions. Explore how to use logic, propositions, true or false, and critical thinking in math problems.
3. Inductive & Deductive Reasoning in Geometry: Definition & Uses
In geometry, inductive reasoning is based on observations, while deductive reasoning is based on facts, and both are used by mathematicians to discover new proofs. Learn about the definition and uses of inductive and deductive reasoning in geometry, and discover that one type of reasoning is based on observations while the other is based on facts.
4. Undefined Terms of Geometry: Concepts & Significance
There are four undefined terms of geometry which are used to formally define other words and theorems and don't require formal definition. Explore the concepts and significance of the point, line, plane, and set as undefined terms.
5. Types of Angles: Vertical, Corresponding, Alternate Interior & Others
Understanding angles and angle relationships allows for easier calculation of angle measurement. Learn how to define various types of angles, including vertical, corresponding, alternate interior angles, and how to calculate degree measurement using angle relationships.
6. Properties and Postulates of Geometric Figures
Postulates are simple truths without formal proof which are used to construct theorems. Learn how these building blocks of mathematical theorems are used to make sense of concepts such as points, lines, and planes.
7. The Axiomatic System: Definition & Properties
In mathematics, the axiomatic system refers to the statements and rules used to develop and prove theorems. Explore the definition and properties of the axiomatic system, including consistency, independence, and completeness. Understand how an axiom compares to an axiomatic system.
8. Algebraic Laws and Geometric Postulates
Algebraic laws show how mathematical operations are performed while geometric postulates are basic truths, which are the foundation for other theorems. Learn about the commutative, associative, distributive, reflexive, symmetric, and transitive laws.
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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