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.
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
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.
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. 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.
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. 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.
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.
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.
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.
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.
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.
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.
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.
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 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