Ch 22: Geometric Laws & Proofs

About This Chapter

Get reacquainted with the foundations of geometry with help from entertaining video lessons presented by expert instructors. Revisit Euclidean geometry, the axiomatic system and more as you prepare to take the FTCE Middle Grades Math assessment.

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.

9 Lessons in Chapter 22: Geometric Laws & Proofs
Test your knowledge with a 30-question chapter practice test
Euclidean Geometry: Definition, History & Examples

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.

Euclid's Axiomatic Geometry: Developments & Postulates

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.

Inductive & Deductive Reasoning in Geometry: Definition & Uses

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.

The Axiomatic System: Definition & Properties

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.

Properties and Postulates of Geometric Figures

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.

Algebraic Laws and Geometric Postulates

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.

Direct Proofs: Definition and Applications

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.

Indirect Proof in Geometry: Definition & Examples

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.

Geometric Proofs: Definition and Format

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken
More Exams
There are even more practice exams available in Geometric Laws & Proofs.

Earning College Credit

Did you know… We have over 220 college courses that prepare you to earn credit by exam that is accepted by over 1,500 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

Other Chapters

Other chapters within the College Preparatory Mathematics: Help and Review course

Support