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

About This Chapter

The Geometric Reasoning chapter of this Explorations in Core Math Geometry Companion Course aligns with the same chapter in the Explorations in Core Math Geometry textbook. These simple and fun video lessons are about five minutes long and help you learn the essential lessons about geometric reasoning, statements and proofs.

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.

13 Lessons in Chapter 2: Explorations in Core Math Geometry Chapter 2: Geometric Reasoning
Test your knowledge with a 30-question chapter practice test
Reasoning in Mathematics: Inductive and Deductive Reasoning

1. 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.

Conditional Statements in 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.

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

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

The Venn diagram was introduced by John Venn. Yes, the Venn diagram is named after a real person! His idea was to show sets in terms of pictures. The Venn diagram is now used in many fields, including mathematics. Let's take a look at John Venn's idea.

Logic Laws: Converse, Inverse, Contrapositive & Counterexample

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.

Logical Math Connectors: Conjunctions and Disjunctions

5. 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.

Reasoning in Mathematics: Connective Reasoning

6. Reasoning in Mathematics: Connective Reasoning

Connective reasoning is reasoning that has an operation, or a way to connect two phrases. The five main logic connectives will be reviewed in this lesson.

Biconditional Statement in Geometry: Definition & Examples

7. 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.

Mathematical Induction: Uses & Proofs

8. Mathematical Induction: Uses & Proofs

Watch this video lesson to learn about mathematical induction and how you can use it to prove mathematical statements. See how it is similar to falling dominoes.

Geometric Proofs: Definition and Format

9. 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.

Linear Pair: Definition, Theorem & Example

10. Linear Pair: Definition, Theorem & Example

In this lesson, we'ill discuss how a linear pair is formed and what characteristics apply to angles that create a linear pair. We'lll also go through a few examples in which we solve for the missing angle. At the end of the lesson, test yourself with a quiz.

What is a Paragraph Proof? - Definition & Examples

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

Writing proofs is an important aspect of mathematical inquiry and discovery. This lesson will discuss one method of writing proofs, the paragraph proof. We will explore some examples and provide some guiding steps you may use to write an effective paragraph proof.

Two-Column Proof in Geometry: Definition & Examples

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

This lesson will discuss one method of writing proofs, the two-column proof. We will explore some examples and provide some guiding steps you may use to write an effective two-column proof.

Flowchart Proof: Definition & Example

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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