About This Chapter
AFOQT: Principles of Geometry - Chapter Summary
Let us help you review basic principles of geometry that are assessed on the Air Force Officer Qualifying Test (AFOQT). You're able to create an individualized learning experience by pre-assessing your knowledge through the multiple-choice quizzes and then complete lessons based on the scores. Concepts covered in these lessons include:
- Geometry history and definitions
- Undefined terms of geometry
- Inductive & deductive reasoning
- Geometric contributions by Thales and Pythagoras
- Axiomatic geometry
- Basic geometric postulates
Each lesson has a short video, that has an interactive timeline, and assessment quizzes that highlight the most important information from the lesson. These assessments can be used to help you determine whether you are ready to advance to the next lesson in the chapter or if you need to review certain parts of the video. You can also check your progress through the study guide with the personal dashboard.
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. 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. 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.
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.
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Other chapters within the AFOQT: Practice & Study Guide course
- AFOQT: Word Comprehension
- AFOQT: Analogies
- AFOQT: Arithmetic Comprehension
- AFOQT: Arithmetic Equations
- AFOQT: Factoring
- AFOQT: Exponents & Roots
- AFOQT: Word Problems
- AFOQT: Algebraic Expressions
- AFOQT: Graphs, Linear Equations & Parabolas
- AFOQT: Quadratic Equations
- AFOQT: Polynomials, Functions & Rational Expressions
- AFOQT: Lines & Angles
- AFOQT: Circles & Triangles
- AFOQT: Rectangles & Solids
- AFOQT: Figures & Polygons
- AFOQT: Three-dimensional Blocks
- AFOQT: Object Visualization & Manipulation
- AFOQT: Table Knowledge
- AFOQT: Instrument Knowledge
- AFOQT: Aviation
- AFOQT: The Metric System & Scientific Notation
- AFOQT: Atoms & Matter
- AFOQT: Thermodynamics & Electricity
- AFOQT: Magnetism
- AFOQT: Earth Science
- AFOQT: Biomolecules & Cells
- AFOQT: Human Anatomy
- AFOQT: Personality Traits & Attitudes
- AFOQT Flashcards