About This Chapter
High School Geometry: Foundations of Geometry - Chapter Summary
Our world is built of shapes, and to gain a deeper understanding of our world, we need a way to measure and examine the shapes. These lessons provide you with the foundational knowledge you will need to comprehend all the geometric shapes, lines, planes, and points around us.
When you use our study materials to review this math topic, remember that we built our site specifically with your needs in mind. For instance, we never require you to make study appointments. Instead, we put all of our information online, giving you full access to our lessons, quizzes, flashcards, and other tools. No matter what time of day or night you like to study, we are here to offer support. When you have finished the lessons in this chapter, you should possess the skills to do the following:
- Explain the definition of geometry
- Apply deductive and inductive reasoning techniques
- Name early mathematicians who contributed to geometry
- Describe the properties of the axiomatic systems
- Identify the postulates and developments of Euclid's axiomatic geometry
- Check out the significance and concepts of undefined geometry terms
- Define theorems and postulates
- Compare the postulates and properties of geometric figures
- Examine geometric postulates and algebraic laws
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. 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. Thales & Pythagoras: Early Contributions to Geometry
In this video lesson, you will learn about the contributions Thales and Pythagoras made to the study of geometry. Also learn which of their major contributions is still in use today.
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. 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.
6. 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.
7. 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.
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.
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Other chapters within the Geometry: High School course
- High School Geometry: Logic in Mathematics
- High School Geometry: Introduction to Geometric Figures
- High School Geometry: Properties of Triangles
- High School Geometry: Triangles, Theorems and Proofs
- High School Geometry: Parallel Lines and Polygons
- High School Geometry: Similar Polygons
- High School Geometry: Quadrilaterals
- High School Geometry: Circular Arcs and Circles
- High School Geometry: Conic Sections
- High School Geometry: Geometric Solids
- High School Geometry: Analytical Geometry
- High School Geometry: Probability
- High School Geometry: Introduction to Trigonometry
- Teacher Resources for High School Geometry