# Ch 2: McDougal Littell Geometry Chapter 2: Reasoning and Proof

### 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

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.

### 2. Conditional Statements in Math

A conditional statement is a type of mathematical logic that uses an if-then structure to combine two statements; however, conditional statements may not make sense in reality. Investigate the parts of a conditional statement, and discover how a statement can be true in the world of logic, but false in the real world.

### 3. Logical Math Connectors: Conjunctions and Disjunctions

Logical math connectors are used to combine two statements with either a conjunction or disjunction. Learn how to recognize statements and discover the importance of connectors and the difference between conjunctions and disjunctions.

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

The validity of a logical statement often can be determined by looking at its logical equivalence. Learn about the logical variants of a conditional statement, and explore the definitions of converse, inverse, contrapositive, and counterexample.

### 5. 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.

### 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. 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.

### 8. The Distributive Property and Algebraic Expressions

The distributive property, which involves distributing a term across all numbers and variables within the parentheses, provides a useful way to simplify algebraic expressions. Learn what the distribution property is, and solve for it in algebraic expressions in practice problems.

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### Other Chapters

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