幾何学：アルフレッド教授による1年間のコース

Welcome to our Geometry Small Group Online Class, an ongoing course where you can join anytime! Each week, we delve into a new and exciting topic in the world of geometry. This class is designed to help you develop a solid understanding of geometric concepts and their applications.

Whether you're a beginner or have some prior knowledge of geometry, our class offers a welcoming environment for all learners. Our experienced instructors present each concept in a step-by-step, easy-to-understand manner, ensuring that you grasp the material effectively. We emphasize interactive learning, with opportunities for active participation, discussions, and engagement with fellow classmates.

In this ongoing class, we cover a wide range of topics throughout the course, including:

Understanding Points, Lines, and Planes
Measuring and Constructing Segments
Measuring and Constructing Angles
Exploring Pairs of Angles
Utilizing Formulas in Geometry
Investigating Midpoint and Distance on the Coordinate Plane
Understanding Transformations in the Coordinate Plane
Using Inductive Reasoning to Make Conjectures
Analyzing Conditional Statements
Exploring Bi-conditional Statements and Definitions
Investigating Algebraic Proof
Examining Geometric Proof
Analyzing Flowchart and Paragraph Proofs
Understanding Lines and Angles
Examining Angles Formed by Parallel Lines
Investigating Angles Formed by Parallel Lines and Transversals
Proving Lines Parallel
Understanding Perpendicular Lines
Analyzing Slopes of Lines
Exploring Lines in the Coordinate Plane
Classifying Triangles
Examining Triangle Congruence using SSS and SAS
Investigating Triangle Congruence using ASA, AAS, and HL
Understanding Triangle Congruence using CPCTC
Introduction to Coordinate Proof
Analyzing Isosceles and Equilateral Triangles
Investigating Perpendicular and Angle Bisectors
Exploring Bisectors of Triangles
Understanding Medians and Altitudes of Triangles
Examining the Triangle Mid-segment Theorem
The class is structured as follows:
We begin each session with warm-up exercises, which are posted on the board. These exercises allow you to actively engage with the material from the moment you enter the class. Afterward, the instructor checks the warm-up exercise and proceeds to present the day's topic. Each concept is explained with illustrative examples, ensuring clarity and understanding. You will have guided and independent practice questions to solidify your mastery of the material.

To enhance your learning experience, we provide challenge activities such as word problems and exercises that are commonly found in SAT/ACT tests. Additionally, we offer extension activities including games, puzzles, and videos, which promote critical thinking and strengthen your analytical skills.

Sometimes, there will be an evaluation to assess your progress. The instructor may also provide recommendations for further study, and optional homework assignments may be offered to reinforce the concepts covered in class.

We value interaction and encourage active participation in our class. You will have the opportunity to interact with the instructor and your peers through discussions, group activities, and sharing different problem-solving approaches. We believe in catering to individual differences and promoting a supportive and inclusive learning environment.

We are committed to your success and aim to provide a comprehensive and enriching learning experience throughout the course.