About This Chapter
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.
|Critical Thinking and Logic in Mathematics||Understand logic, arguments, premises and conclusions.|
|Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice||Learn about false cause, hasty generalization, limited choice and circular reasoning.|
|Logical Fallacies: Appeals to Ignorance, Emotion or Popularity||Explore appeal to popularity, appeal to ignorance and appeal to emotion.|
|Propositions, Truth Values and Truth Tables||Learn about propositions, truth values, negation and truth tables.|
|Logical Math Connectors: Conjunctions and Disjunctions||Explore conjunctions and disjunctions as well as the inverse and converse of conditional statements.|
|Conditional Statements in Math||Understand conditional propositions, hypotheses, conclusions and alternative phrasing of conditionals.|
|Logical Equivalence: Converse, Inverse, Contrapostive & Counterexample||Learn the meaning of converse, inverse, contrapositive and logically equivalent.|
|Direct Proofs||Explore direct proofs and ways they appear in math.|
|Geometric Proofs: Definition and Format||Learn about geometric proofs and the format of formal proofs.|
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.
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.
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.
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.
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. 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.
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.
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.
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.
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Other chapters within the Geometry: High School course
- High School Geometry: Foundations of Geometry
- High School Geometry: Introduction to Geometric Figures
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Conic Sections
- High School Geometry: Geometric Solids
- High School Geometry: Analytical Geometry
- High School Geometry: Probability
- High School Geometry: Introduction to Trigonometry