Free online courseGeometry

Course Description

The Geometry course spans 37 hours and 8 minutes of comprehensive content aimed at providing a solid foundation in the subject of Geometry. The course has garnered exceptional reviews, achieving an impressive average rating of 5 out of 5 stars, reflecting its high quality and the satisfaction of its learners. This course is categorized under Basic Studies, with a specific focus on Geometry.

The course delves into fundamental geometric concepts starting with Geometry 1.2 and progresses through various topics such as angles, postulates, and theorems. Each section builds upon the previous one, ensuring a progressive learning curve that reinforces understanding and application of geometric principles.

One of the strengths of this course is its meticulous coverage of logical reasoning in geometry. Learners are introduced to if-and-then statements, properties from algebra, and techniques for proving theorems. This logical framework is essential for solving complex geometric problems and forms a critical component of the curriculum.

Special pairs of angles and perpendicular lines are thoroughly explored, followed by planning and constructing geometric proofs. The course incorporates hands-on geometry constructions, providing practical experience in applying theoretical knowledge.

Parallel lines, triangles, polygons, and their respective properties are discussed in depth. Students will gain a comprehensive understanding of congruent figures and various methods to prove triangle congruence. Special theorems related to isosceles triangles and the application of congruent triangles are also covered, enabling learners to tackle diverse geometric challenges.

The course also focuses on quadrilaterals and their properties, including parallelograms, trapezoids, and inequalities within geometric figures. Various statements such as inverses, contrapositives, and proofs by contradiction are explained, adding to the learner's toolkit for logical reasoning in geometry.

The later sections of the course transition into ratios, proportions, and the concept of similarity, especially within triangles and right triangles. The Pythagorean Theorem, its converse, and special right triangles receive significant attention along with trigonometric ratios and their applications in right triangle trigonometry.

Understanding circles, tangents, arcs, and central angles forms another key component of the curriculum. The course extends this knowledge to practical matters such as areas of various geometric figures, including rectangles, parallelograms, trapezoids, regular polygons, and circles. Geometric probability is introduced to apply these concepts to real-world scenarios.

Advanced topics in three-dimensional geometry include prisms, pyramids, cylinders, cones, and spheres, examining their areas and volumes. The distance formula, slope of a line, parallel and perpendicular lines, as well as vectors, midpoints, and graphing linear equations are comprehensively covered within coordinate geometry.

The course concludes with mappings and functions, reflections, translations, rotations, dilations, and composite mappings. Symmetry in the plane and space is explored, along with practical drawing techniques using lines and curves, making this Geometry course a thorough and engaging educational experience.