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
The lesson will explore the history and nature of Euclidean geometry, including its origins in Alexandria under Euclid and its five postulates. Its influence on the work of other mathematicians will also be covered.
2. Euclid's Axiomatic Geometry: Developments & Postulates
Learn how the way we do proofs in geometry had its start with Euclid in this video lesson. Learn about his contributions to the geometry we know today. Also learn about the five basic truths that he used as a basis for all other teachings.
3. Inductive & Deductive Reasoning in Geometry: Definition & Uses
Watch this video lesson, and you will learn how important inductive and deductive reasoning is in the field of mathematics, especially when dealing with proofs in geometry. Learn how these two fundamental forms of reasoning give rise to formal theorems.
4. The Axiomatic System: Definition & Properties
Learn what kinds of things are included in an axiomatic system in this video lesson. Also learn why consistency, independence, and completeness are important in axiomatic systems.
5. Properties and Postulates of Geometric Figures
In geometry, there are some basic postulates that are relied upon as the basis for other theorems. Watch this video to learn about the postulates that deal with points, lines, and planes.
6. Algebraic Laws and Geometric Postulates
Watch this video to learn about the basic algebraic laws that are also part of the basic geometric postulates that form the basis for the geometry that we know and study today.
7. 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.
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
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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