About This Chapter
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- Begin your assignment or other geometry work.
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- Define geometry.
- Understand how to use inductive and deductive reasoning in geometry.
- Examine Thales's and Pythagoras's early contributions to geometry.
- List the properties of the axiomatic system.
- Discuss Euclid's axiomatic geometry.
- Explain the significance of undefined terms of geometry.
- Learn about postulates and theorems.
- Describe the properties and postulates of geometric figures.
- Take a look at algebraic laws and geometric 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.
9. Opposite Rays in Geometry: Definition & Example
This lesson will teach you the definition of opposite rays. You will be given a couple of examples. Then, you will be able to test yourself with a quiz.
10. Secant Line: Definition & Formula
In this lesson, we'll learn what a secant line is and how to find its equation. We'll also look at some examples of secant lines in the world around us.
11. Tangent Line: Definition & Equation
In this lesson, we explore the idea and definition of a tangent line both visually and algebraically. After learning how to calculate a tangent line to a curve, you will find a short quiz to test your knowledge.
12. What Are Intersecting Lines? - Definition & Examples
In this lesson, you'll learn the geometric definition of a line. You'll also learn what intersecting lines are and view a few examples of them. Then, you can test your knowledge in a brief quiz.
13. Aliquot Part: Definition & Examples
In this lesson, we will look at the definition of an aliquot part of a number. We will explore how it relates to division and is actually the same thing as a well-known concept within division.
14. How to Construct an Angle Trisection
Let's discuss what an angle trisection is and how to construct one using just a marked straightedge and a compass. We will also look at a proof solidifying the fact that the construction process does create an angle trisection.
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Other chapters within the NY Regents Exam - Geometry: Tutoring Solution course
- NY Regents - Logic in Mathematics: Tutoring Solution
- NY Regents - Introduction to Geometric Figures: Tutoring Solution
- NY Regents - Similar Polygons: Tutoring Solution
- NY Regents - Quadrilaterals: Tutoring Solution
- NY Regents - Circular Arcs and Circles: Tutoring Solution
- NY Regents - Analytical Geometry: Tutoring Solution
- NY Regents - Triangles and Congruency: Tutoring Solution
- NY Regents - Parallel Lines and Polygons: Tutoring Solution
- NY Regents - Geometric Solids: Tutoring Solution