Free online courseGeometry Course

Course Description

The Geometry Course offers a comprehensive exploration into the fundamentals of geometry. Spanning a duration of 15 hours and 57 minutes, this course is meticulously designed for students beginning their journey in the realm of geometric concepts. Currently without any reviews, this course falls under the Basic Studies category and delves deeply into the subcategory of Geometry.

This course begins with the foundational elements of geometry, introducing students to the basic constructs such as points, lines, and planes. As you progress, you'll engage with the concepts of line segments and distance, which are essential for understanding spatial relationships. The Midpoint Formula is also covered early on to help in determining central points between line segments.

An essential aspect of geometry—the measurement of angles—is addressed thoroughly, including various angle relationships that are fundamental to understanding geometric figures. Transitioning from two-dimensional figures to three-dimensional ones prepares students for more complex applications and visualizations of geometric principles.

The course then delves into logical reasoning, starting with inductive reasoning and proofs. Understanding the fundamentals of logic and conditional statements is crucial for developing a strong foundation in mathematical reasoning. This section also covers proving segment and angle relationships, which are vital skills in geometric problem-solving.

Lines and their properties form the backbone of many geometric principles. The course explores parallel lines, transversals, and the angles they create. The relationship between line slopes and how to write equations of lines is also examined. Understanding how to prove lines parallel and the concepts of perpendiculars and distance are included to provide a rounded comprehension of line geometry.

Triangles, one of the most studied shapes in geometry, are given particular attention. This includes classifying triangles, understanding their angles, and proving them congruent through various methods such as Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Angle-Angle-Side (AAS). Special types of triangles like isosceles and equilateral are also discussed. Further, the course delves into the properties of bisectors, medians, altitudes, and inequalities within triangles, as well as the triangle inequality theorem and inequalities in two triangles.

Students will gain significant insight into polygons by learning about their angles and properties. Parallelograms and tests for identifying them are another vital component of this section. Ratio and proportion principles are then applied to polygons and triangles, exploring similarity and transformations, including scale drawings and models.

Key principles such as the Geometric Mean, the Pythagorean Theorem and its converse, and special right triangles set the stage for more advanced topics like trigonometry, angles of elevation and depression, and the laws of sines and cosines. Vectors are also introduced to enhance understanding of direction and magnitude in geometry.

The course includes a thorough examination of geometric transformations, such as reflections and translations. Circles also play a crucial role, and you'll learn about their circumference, measuring angles and arcs, arcs and chords, inscribing angles, and tangents.

In conclusion, this Geometry Course provides a broad and detailed foundation in geometric principles, making it an excellent starting point for those in Basic Studies seeking to deepen their knowledge in Geometry. Whether it's mastering the properties of shapes, understanding geometric transformations, or applying trigonometric principles, this course offers a structured path to become proficient in geometry.