About This Chapter
Who's it for?
This unit of our High School Geometry Homeschool course will benefit any student who is trying to learn about high school geometry basics. There is no faster or easier way to learn about geometry. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn inductive and deductive reasoning, postulates and theorems, algebraic laws and geometric postulates.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a geometry curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and a basic geometry unit exam confirm understanding or identify any topics that require review.
Foundations of Geometry Unit Objectives:
- Describe the field of geometry.
- Describe how to use inductive and deductive reasoning for geometry.
- State Thales' and Pythagoras' contributions to geometry.
- List the properties of an axiomatic system.
- Discuss how Euclid of Alexandria contributed to geometry.
- Define postulates and theorems and what they're used for.
- Apply postulates to points, lines, planes and real numbers.
- List algebraic laws and how they're used in conjunction with postulates.
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 High School Geometry: Homeschool Curriculum course
- Logic in Mathematics: Homeschool Curriculum
- Geometric Figures: Homeschool Curriculum
- Properties of Triangles: Homeschool Curriculum
- Triangles, Theorems & Proofs: Homeschool Curriculum
- Parallel Lines & Polygons: Homeschool Curriculum
- Similar Polygons: Homeschool Curriculum
- Quadrilaterals: Homeschool Curriculum
- Circular Arcs and Circles: Homeschool Curriculum
- Focus & Directrix: Homeschool Curriculum
- Geometric Solids: Homeschool Curriculum
- Analytical Geometry: Homeschool Curriculum
- Introduction to Trigonometry: Homeschool Curriculum