About This Chapter
Below is a sample breakdown of the Foundations of Geometry chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
|Day||Topics||Key Terms and Concepts Covered|
|Monday||Geometry Definitions and Reasoning||The origins of geometry, and drawing conclusions from various facts and observations|
|Tuesday||Thales, Pythagoras and the Axiomatic System||The contributions of early mathematicians, and deriving theorems with the axiomatic system|
|Wednesday||Axiomatic Geometry and Undefined Terms||The logical system of Euclid, planes, sets, and lines|
|Thursday||Postulates, Theorems and Geometric Figures||The purpose of postulates and theorems, and working with lines, planes, and points|
|Friday||Algebraic Laws and Geometric Postulates||Study the distributive, transitive, reflexive and symmetric laws, as well as other algebraic laws|
1. 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.
2. 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.
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. 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. 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.
7. 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.
8. 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.
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Other chapters within the Geometry Curriculum Resource & Lesson Plans course
- Logic in Mathematics Lesson Plans
- Introduction to Geometric Figures Lesson Plans
- Properties of Triangles Lesson Plans
- Triangles, Theorems & Proofs Lesson Plans
- Parallel Lines & Polygons Lesson Plans
- Similar Polygons Lesson Plans
- Quadrilaterals Lesson Plans
- Circular Arcs & Circles Lesson Plans
- Conic Sections Lesson Plans
- Geometric Solids Lesson Plans
- Analytical Geometry Lesson Plans
- Introduction to Trigonometry Lesson Plans