About This Chapter
How it works:
- Identify the lessons in the McDougal Littell Geometry Textbook Reasoning and Proof chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the reasoning and proof 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:
- Critical thinking and logic in mathematics
- Conditional statements in math
- Rewriting conditional statements in if-then form
- Logical math connectors: conjunctions and disjunctions
- Logical equivalence: converse, inverse, contrapositive and counterexample
- Writing postulates about points, lines and planes using conditional statements
- Biconditional statements
- Using symbolic notation
- Inductive and deductive reasoning in geometry
- The law of detachment
- The law of syllogism
- Properties and postulates of geometric figures
- Algebraic laws and geometric postulates
- The distributive property and algebraic expressions
- Using properties of length and measure
- Properties of segment congruence
- Writing a paragraph proof
- Using congruence of segments
- Properties of angle congruence
- Right angle congruence theorem
- Congruent supplements theorem
- Congruent complements theorem
- Linear pair postulate
- Vertical angles theorem
McDougal Littell Geometry is a registered trademark of McDougal Littell, which is not affiliated with Study.com.
1. 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.
2. Conditional Statements in Math
Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.
3. Logical Math Connectors: Conjunctions and Disjunctions
Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.
4. 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.
5. 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.
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. 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.
8. The Distributive Property and Algebraic Expressions
The order of operations is great. But sometimes we need to bend the rules to simplify an equation. Fortunately, the distributive property gives us a scenario in which this is okay. Learn all about it in this lesson.
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Other chapters within the McDougal Littell Geometry: Online Textbook Help course
- McDougal Littell Geometry Chapter 1: Basics of Geometry
- McDougal Littell Geometry Chapter 3: Perpendicular and Parallel Lines
- McDougal Littell Geometry Chapter 4: Congruent Triangles
- McDougal Littell Geometry Chapter 5: Properties of Triangles
- McDougal Littell Geometry Chapter 6: Quadrilaterals
- McDougal Littell Geometry Chapter 7: Transformations
- McDougal Littell Geometry Chapter 8: Similarity
- McDougal Littell Geometry Chapter 9: Right Triangles and Trigonometry
- McDougal Littell Geometry Chapter 10: Circles
- McDougal Littell Geometry Chapter 11: Area of Polygons and Circles
- McDougal Littell Geometry Chapter 12: Surface Area and Volume