# Ch 2: Big Ideas Math Geometry Chapter 2: Reasoning and Proofs

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Reasoning and Proofs chapter of your textbook.
- Watch fun videos that cover the reasoning and proofs concepts you need to learn or review.
- Complete the quiz after watching each video lesson 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.

## Chapter Topics

You'll learn all of the geometry topics covered in the textbook chapter, including:

- Examples of line segments
- Mathematical reasoning
- Geometric figures and diagrams
- Geometric properties
- Geometric proof format

*Big Ideas Math is a registered trademark of Larson Texts, Inc., which is not affiliated with Study.com.*

### 1. 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.

### 2. Biconditional Statement in Geometry: Definition & Examples

In this lesson, you'll learn how to define and recognize a biconditional statement. We'll review conditional statements and their converses and look at examples of each. We'll also discuss the criteria for writing biconditional statements.

### 3. Propositions, Truth Values and Truth Tables

Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.

### 4. Reasoning in Mathematics: Inductive and Deductive Reasoning

Many people think that deductive and inductive reasoning are the same thing. It is assumed these words are synonymous. They are not. This lesson reveals the reality of these two types of reasoning.

### 5. 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.

### 6. Addition Property of Equality: Definition & Example

After watching this video lesson, you should be able to use the addition property of equality to help you solve problems. In addition, you can learn the formula for this property.

### 7. Subtraction Property of Equality: Definition & Example

In this video lesson, we look at the subtraction property of equality. Learn how it helps you to solve problems and how it keeps equations the same. Learn what you must do to both sides of an equation.

### 8. Multiplication Property of Equality: Definition & Example

After watching this video lesson, you will learn to use the multiplication property of equality to help you solve problems in math. You will also learn the formula for this property.

### 9. Division Property of Equality: Definition & Example

In this video lesson, you will learn about the division property of equality, its formula, and how you can use it to help you solve problems where you are looking for an unknown number.

### 10. Symmetric Property of Equality: Definition & Examples

Have you ever finished a math problem only to see that the teacher's answer was written backwards? Find out why your answer is correct in this lesson on the symmetric property of equality!

### 11. Transitive Property of Equality: Definition & Example

After watching this video lesson, you will understand how the transitive property of equality works when you have two equations that are equal to each other. Learn the formula for this property and how you can use it to help you solve problems.

### 12. The Reflexive Property of Equality: Definition & Examples

In this lesson, we will review the definition of the reflexive property of equality. We will also look at why this property is important. Following the lesson will be a brief quiz to test your knowledge on the reflexive property of equality.

### 13. 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.

### 14. 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.

### 15. Congruence Properties of Line Segments & Angles

This lesson discusses the concept of congruence with the help of relevant examples. You will also learn about the reflexive, symmetric and transitive properties of congruence related to line segments and angles.

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### Other Chapters

Other chapters within the Big Ideas Math Geometry: Online Textbook Help course

- Big Ideas Math Geometry Chapter 1: Basics of Geometry
- Big Ideas Math Geometry Chapter 3: Parallel and Perpendicular Lines
- Big Ideas Math Geometry Chapter 4: Transformations
- Big Ideas Math Geometry Chapter 5: Congruent Triangles
- Big Ideas Math Geometry Chapter 6: Relationships Within Triangles
- Big Ideas Math Geometry Chapter 7: Quadrilaterals and Other Polygons
- Big Ideas Math Geometry Chapter 8: Similarity
- Big Ideas Math Geometry Chapter 9: Right Triangles and Trigonometry
- Big Ideas Math Geometry Chapter 10: Circles
- Big Ideas Math Geometry Chapter 11: Circumference, Area, and Volume
- Big Ideas Math Geometry Chapter 12: Probability