About This Chapter
Ohio EOCE Integrated Math I: Foundations of Geometry - Chapter Summary
When studying for the Ohio EOCE - Integrated Math I exam, it's good to feel ready to answer just about any question you face. This chapter can ensure you're ready for questions that address the foundations of geometry. Review lessons that explore the axiomatic system, arc length, geometric postulates and more. Once finished, you will be prepared for the following on the exam:
- Defining geometry, and explaining the significance of undefined terms of geometry
- Sharing the meaning and properties of the axiomatic system
- Discussing developments and postulates of Euclid's axiomatic geometry
- Identifying properties and postulates of geometric figures
- Understanding properties of circles
- Describing angles formed by a transversal
- Providing details about algebraic laws and geometric postulates
The video and text lessons in this chapter are flexible and can be viewed in any sequence that suits your current knowledge of the foundations of geometry. If you want to test your current knowledge, feel free to take the self-assessment quiz with each lesson, which can gauge your need to review the lessons. When watching video lessons, take advantage of clickable video tags that allow you to identify and skip to key topics without watching videos in full. To ensure you're prepared for foundations of geometry questions on the day of the test, take the practice chapter exam that reinforces concepts covered in the lessons.
1. What is Geometry?
Geometry can be traced all the way back to 2000 BC. Watch this video lesson and learn how much geometry has grown over time, and how people from Egypt, Greece, and France have contributed to the geometry we now use today.
2. Undefined Terms of Geometry: Concepts & Significance
What do points, lines, planes, and sets have in common? Watch this video lesson to find out what they are, what they look like, and why they are called undefined terms.
3. 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.
4. 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.
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. Properties of Shapes: Circles
Circles are fundamental to everything we do. But, did you know they're much more than just round shapes? In this lesson, we'll look at the various parts of circles and how they all relate.
7. Angles Formed by a Transversal
When you have a pair of parallel lines and a transversal, something very interesting happens to the angles that are formed. You can see this happen in real life at street intersections and such. Watch this video lesson to learn about all of this.
8. 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.
9. Arc Length: Definition & Equation
Arc length is an important aspect to understanding portions of curved lengths. As you will learn in this lesson, combining our knowledge of circumference and central angle measures allows us to find arc length.
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Other chapters within the Ohio End of Course Exam - Integrated Math I: Test Prep & Practice course
- Ohio EOCE Integrated Math I: Basic Math
- Ohio EOCE Integrated Math I: Decimals & Percents
- Ohio EOCE Integrated Math I: Inequalities
- Ohio EOCE Integrated Math I: Solving Linear Equations
- Ohio EOCE Integrated Math I: Systems of Linear Equations
- Ohio EOCE Integrated Math I: Distributing Terms in Algebra
- Ohio EOCE Integrated Math I: Exponents
- Ohio EOCE Integrated Math I: Polynomials
- Ohio EOCE Integrated Math I: Rational Expressions
- Ohio EOCE Integrated Math I: FOIL & Quadratic Equations
- Ohio EOCE Integrated Math I: Functions Overview
- Ohio EOCE Integrated Math I: Matrices & Absolute Value
- Ohio EOCE Integrated Math I: Square Roots
- Ohio EOCE Integrated Math I: Basic Algebra
- Ohio EOCE Integrated Math I: Rotations
- Ohio EOCE Integrated Math I: Theorems & Proofs
- Ohio EOCE Integrated Math I: Complex Numbers
- Ohio EOCE Integrated Math I: Exponential & Logarithmic Expressions
- Ohio EOCE Integrated Math I: Factorials & Binomial Theory
- Ohio EOCE Integrated Math I: Sequences & Series
- Ohio End of Course Exam - Integrated Math I Flashcards