# Ch 2: Explorations in Core Math Geometry Chapter 2: Geometric Reasoning

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Geometric Reasoning chapter of your textbook.
- Watch fun videos that cover the geometric reasoning 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:

- Inductive and deductive reasoning
- Conditional statements and bioconditional statements
- Venn diagrams
- Logical equivalence
- Geometric proofs

*Explorations in Core Math is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

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

Inductive and deductive reasoning are two methods of reasoning used in mathematics. Explore the definitions of inductive and deductive reasoning, review examples of each in action, and learn when and how to use them.

### 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. Venn Diagrams: Subset, Disjoint, Overlap, Intersection & Union

Venn diagrams show the relationships and operations between a collection of elements. Learn about the concepts and operations that can be illustrated in a Venn diagram, such as subsets, disjoints, overlaps, intersections, unions, and complements.

### 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. 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.

### 6. Reasoning in Mathematics: Connective Reasoning

Connective reasoning connects compound statements in mathematics. Learn about connective reasoning, the logical connectives such as negation, conjunction, disjunction, conditional, and biconditional, and differentiate conjunction and disjunction.

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

A biconditional statement in geometry is a true statement that combines a hypothesis and conclusion with the words 'if and only if' instead of the words 'if' and 'then'. Explore the definition and examples of biconditional statements and learn about conditional and converse statements.

### 8. Mathematical Induction: Uses & Proofs

In mathematics, induction is a method of proving the validity of a statement asserting that all cases must be true provided the first case was true. Learn how the uses and proofs of mathematical induction can determine the validity of a mathematical statement.

### 9. 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.

### 10. Linear Pair: Definition, Theorem & Example

In geometry, a linear pair is a set of adjoining angles with degrees that total 180. Explore the definition, theorem, example, and application of linear pairs. Understand the concepts of adjacent and supplementary in linear pairs, and recognize the importance of lines.

### 11. What is a Paragraph Proof? - Definition & Examples

Paragraph Proofs are logical arguments presented in factual statements to determine a specific conclusion in a written paragraph. Using provided examples, learn the steps and outline of effective paragraph proofs.

### 12. Two-Column Proof in Geometry: Definition & Examples

Arranging the facts in logical order is necessary to prove something and, in math, these proofs can be written in a multiple ways. Learn the three main types of proofs, what makes up a two-column proof table, and how to use the two-column method effectively.

### 13. Flowchart Proof: Definition & Example

This lesson will provide a definition of a flowchart proof. It will also provide an example of how to use a flowchart proof by proving the vertical angles theorem.

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### Other Chapters

Other chapters within the Explorations in Core Math - Geometry: Online Textbook Help course

- Explorations in Core Math Geometry Chapter 1: Foundations for Geometry
- Explorations in Core Math Geometry Chapter 3: Parallel and Perpendicular Lines
- Explorations in Core Math Geometry Chapter 4: Triangle Congruence
- Explorations in Core Math Geometry Chapter 5: Properties and Attributes of Triangles
- Explorations in Core Math Geometry Chapter 6: Polygons and Quadrilaterals
- Explorations in Core Math Geometry Chapter 7: Similarity
- Explorations in Core Math Geometry Chapter 8: Right Triangles and Trigonometry
- Explorations in Core Math Geometry Chapter 9: Extending Transformational Geometry
- Explorations in Core Math Geometry Chapter 10: Extending Perimeter, Circumference and Area
- Explorations in Core Math Geometry Chapter 11: Spatial Reasoning
- Explorations in Core Math Geometry Chapter 12: Circles
- Explorations in Core Math Geometry Chapter 13: Probablity