Login

Ch 2: High School Geometry: Logic in Mathematics

About This Chapter

Watch logic in mathematics video lessons and learn about conditional statements in geometry, truth tables and geometric proofs. Take quick quizzes to make sure you fully understand logic in mathematics.

High School Geometry: Logic in Mathematics - Chapter Summary and Learning Objectives

To write a geometric proof, students must be able to advance logically and systematically from the proof's premise to its conclusion. Before they can do this, they must understand what logic statements are and how they apply to geometry. At the end of this chapter, you should be able to:

  • Use conditional statements in relation to geometry.
  • Explain the difference between a conjunction and a disjunction.
  • Identify the inverse and converse of conditional statements.
  • Display truth values for statements by creating a truth table.
  • Write geometric proofs.

VideoObjective
Critical Thinking and Logic in MathematicsUnderstand logic, arguments, premises and conclusions.
Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited ChoiceLearn about false cause, hasty generalization, limited choice and circular reasoning.
Logical Fallacies: Appeals to Ignorance, Emotion or PopularityExplore appeal to popularity, appeal to ignorance and appeal to emotion.
Propositions, Truth Values and Truth TablesLearn about propositions, truth values, negation and truth tables.
Logical Math Connectors: Conjunctions and DisjunctionsExplore conjunctions and disjunctions as well as the inverse and converse of conditional statements.
Conditional Statements in MathUnderstand conditional propositions, hypotheses, conclusions and alternative phrasing of conditionals.
Logical Equivalence: Converse, Inverse, Contrapostive & CounterexampleLearn the meaning of converse, inverse, contrapositive and logically equivalent.
Direct ProofsExplore direct proofs and ways they appear in math.
Geometric Proofs: Definition and FormatLearn about geometric proofs and the format of formal proofs.

9 Lessons in Chapter 2: High School Geometry: Logic in Mathematics
Critical Thinking and Logic in Mathematics

1. Critical Thinking and Logic in Mathematics

Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.

Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

2. Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

Watch this video lesson to see how you can identify cases where logic is not sound. Learn the characteristic traits of hasty generalization, circular reasoning, false cause, and limited choice.

Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

3. Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

Watch this video lesson to see examples of the logical fallacies of appeals to ignorance, emotion, and popularity. You will also see how to identify them.

Propositions, Truth Values and Truth Tables

4. 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.

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.

Conditional Statements in Math

6. 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.

Logic Laws: Converse, Inverse, Contrapositive & Counterexample

7. 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.

Direct Proofs: Definition and Applications

8. Direct Proofs: Definition and Applications

In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.

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.

Earning College Credit

Did you know… We have over 79 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Support