About This Chapter
Who's It For:
Anyone who needs help learning or mastering basic geometry proofs material will benefit from the lessons in this chapter. There is no faster or easier way to learn the fundamentals of geometry proofs. Among those who would benefit are:
- Students who have fallen behind in understanding the fundamentals of geometry proofs
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about the fundamentals of geometry proofs
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How It Works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Fundamentals of Geometry Proofs chapter exam.
Why It Works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Fundamentals of Geometry Proofs chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any question about the fundamentals of geometry proofs. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students Will Review:
This chapter helps students review the concepts in a fundamentals unit of a geometry proofs course. Topics covered include:
- Euclid's axiomatic geometry
- Inductive and deductive reasoning
- Geometric postulates and properties
- The role of critical thinking and logic in math
- Mathematical examples of logical equivalencies
- Using the converse of a statement in math
- Definitions, format and applications of direct and geometric proofs
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. Converse of a Statement: Explanation and Example
Just because a conditional statement is true, is the converse of the statement always going to be true? In this lesson, we'll learn the truth about the converse of statements.
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.
10. Who is Euclid? - Biography, Contribution & Theorems
In this lesson, you'll explore the life and achievements of the Greek mathematician Euclid, and test your understanding about Ancient Greece, early math, and the principles of Euclidean geometry.
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