Ch 22: Geometric Laws & Proofs
About This Chapter
FTCE Middle Grades Math: Foundations of Geometry - Chapter Summary
Utilize the resources in this chapter to make sure you're able to answer questions related to the foundations of geometry on the FTCE Middle Grades Math assessment. Reviewing the lessons in this chapter will prepare you for the following on the exam:
- Defining and explaining the history of Euclidean geometry
- Sharing the developments and postulates of Euclid's axiomatic geometry
- Explaining inductive and deductive reasoning in geometry
- Describing the axiomatic system and properties and postulates of geometric figures
- Discussing algebraic laws and geometric postulates
- Providing the meaning of direct and indirect proofs in geometry
- Showcasing your knowledge of the definition and format of geometric proofs
Strengthen your comprehension of the foundations of geometry by reviewing the lessons in the manner that suits you best. Watch fun video lessons with entertaining visual and audio effects, or explore full transcripts with helpful vocabulary words. Enjoy the ability to revisit the lessons with zero limitations. When you're ready, take self-assessment quizzes and a chapter exam to gauge your knowledge of the lessons. Any questions you have about lesson topics can be submitted to our experts.
1. Euclidean Geometry: Definition, History & Examples
Euclidean geometry, attributed to the Greek mathematician Euclid, is the study of planes and geometrical figures according to axioms and theorems based on Euclid's postulates. Discover the origin and examples of Euclidean geometry, explore the basics of Euclidean geometry, and understand the importance of Euclid's legacy.
2. Euclid's Axiomatic Geometry: Developments & Postulates
Euclid was a Greek mathematician who developed axiomatic geometry based on five basic truths. Study the developments and postulates of Euclid, the axiomatic system, and Euclidean geometry.
3. Inductive & Deductive Reasoning in Geometry: Definition & Uses
In geometry, inductive reasoning is based on observations, while deductive reasoning is based on facts, and both are used by mathematicians to discover new proofs. Learn about the definition and uses of inductive and deductive reasoning in geometry, and discover that one type of reasoning is based on observations while the other is based on facts.
4. The Axiomatic System: Definition & Properties
In mathematics, the axiomatic system refers to the statements and rules used to develop and prove theorems. Explore the definition and properties of the axiomatic system, including consistency, independence, and completeness. Understand how an axiom compares to an axiomatic system.
5. Properties and Postulates of Geometric Figures
Postulates are simple truths without formal proof which are used to construct theorems. Learn how these building blocks of mathematical theorems are used to make sense of concepts such as points, lines, and planes.
6. Algebraic Laws and Geometric Postulates
Algebraic laws show how mathematical operations are performed while geometric postulates are basic truths, which are the foundation for other theorems. Learn about the commutative, associative, distributive, reflexive, symmetric, and transitive laws.
7. Direct Proofs: Definition and Applications
In mathematics, direct proof is a tool used to show if a conditional statement is true or false. Learn how to define a conditional statement and how to use applications of direct proof to determine if a conditional statement is true or false.
8. Indirect Proof in Geometry: Definition & Examples
There are many different methods that can be used to prove a given theory. One of those methods is indirect proof. In this lesson, we will explore indirect proof and learn the steps taken to use this method to prove a given theory.
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.
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Other Chapters
Other chapters within the College Preparatory Mathematics: Help and Review course
- Math Foundations: Help and Review
- Problem Solving & Reasoning Skills
- Percents in Math Basics
- Decimals & Fractions Overview
- Understanding Fractions & Mixed Numbers
- Linear Equations: Help and Review
- Solving and Graphing Inequalities: Help and Review
- Graphing and Factoring Quadratic Equations: Help and Review
- Complex and Imaginary Numbers: Help and Review
- Properties of Exponents: Help and Review
- Praxis I Math: Square Roots
- Properties of Polynomial Functions: Help and Review
- Simplifying and Solving Rational Expressions: Help and Review
- Praxis I Math: Algebraic Expressions
- Properties of Functions: Help and Review
- Logarithms and Exponential Equations: Help and Review
- Data & Estimation
- Logic in Math: Help and Review
- Sets: Help and Review
- Basic Probability and Statistics: Help and Review
- Praxis I Math: Basic Statistics and Probability
- Grade Level Math Vocabulary: Help and Review
- MTEL Middle School Math/Science: History of Geometry
- MTEL Middle School Math/Science: Geometric Properties & Theorems
- MTEL Middle School Math/Science: Principles of Geometry
- MTEL Middle School Math/Science: Algebraic Applications in Geometry
- MTEL Middle School Math/Science: Using Trigonometric Functions
- MTEL Middle School Math/Science: Trigonometric Identities
- MTEL Middle School Math/Science: Trigonometric Applications
- Praxis I Math: Ratio and Proportions
- Praxis I Math: Congruence and Similarity
- Praxis I Math: Geometric Measurement and Dimension