Online Class: Geometry 101 — Beginner to Intermediate Level

Geometry is at the heart of both practical tasks and theoretical studies, explored here from the basics of points and lines to the complexities of polygons and circles. With hands-on lessons in drawing and problem-solving, students finish with the skills to tackle real-world geometry challenges and a primer on trigonometry.

Self-Paced, Online Class
Library Subscription
 
  • 15
    Lessons
  • 27
    Exams &
    Assignments
  • 17
    Hours
    average time
  • 1.7
    CEUs
 
 
 

Course Description

Imagine a world without shape or form, where chaos reigns, and the beauty of symmetry is absent. It's our uncanny ability to interpret the language of geometry that disentangles our perception and breathes order into our universe. Geometry 101 is not merely a course; it's an odyssey through the mathematical symphony that orchestrates the dance of points, lines, and planes, transforming the abstract into the tangible. This course is your gateway to unraveling the vast tapestry of spatial intelligence and leveraging it to enrich every facet of your life.

Step forward into a world where walls whisper stories of angles, where streets and skyscrapers pulse with the logic of lines and shapes. With Geometry 101, you are about to embark on an unforgettable journey, where your guide is not just knowledge, but the power to see the world through a lens of elegance and precision that only geometry can provide.

Each unit of this immersive course is crafted meticulously to weave a seamless tapestry from the rudiments of geometric principles to the nuanced symphony of spatial reasoning. You will begin your exploration with simple points and lines, nurturing your innate curiosity about how these simple constructs form the essence of everything. Soon, you will find yourself navigating the complex interplay of angles and intersections, developing the keen eye necessary to recognize the universe's subtle geometric rhythm.

Venturing into the realm of polygons, you will unravel the mystique of triangles and quadrilaterals, breathing life into these foundational forms. You'll learn to harness their properties, cultivating an understanding as timeless as the pyramids, as profound as the humble honeycomb's hexagonal perfection. This mastery will elevate your capacity to seamlessly transition to the more sophisticated art of constructing and deconstructing composite shapes--an architectural dance of creativity and logic.

The journey doesn't stop at two dimensions. With Geometry 101, you transcend the boundaries of the flat surface. Our exploration ascends into three-dimensional space, offering profound insights into the solid realities of spheres, polyhedra, and the kaleidoscopic interplay of planes. Learn to dissect complexity with clarity and precision, as you unravel the mysteries of volumes and surfaces that define not just objects but the very nature of the space they inhabit.

But why merely follow others? Why not grasp the reins of your geometric destiny and conjure your own constructs? Geometry 101 equips you with this power, taking you beyond theoretical realms to the time-honored art of classical construction. With a compass and straightedge, your sketches evolve from rudimentary lines to masterpieces of innovation and precise beauty--a dance of geometry that transcends mere calculation.

Geometry 101 isn't just about learning; it's about transformation. It's about cultivating a mindset that recognizes the unseen bonds between the abstract world of numbers and the tactile experiences of reality. By the end of this course, you'll possess not only the mathematical prowess to solve geometric conundrums but the confidence to apply this knowledge in real-world scenarios. Your newfound skills in trigonometry will embolden you to navigate a world layered with geometric challenges, whether in technology, design, or day-to-day problem-solving.

Choose Geometry 101 and don't just study geometry--inhabit it. Let it reshape your perspective, refine your talents, and redefine excellence. This course is not just an educational endeavor but the laying of fertile ground where curiosity flowers into mastery. Let Geometry 101 steer you toward the future you're dreaming of--join us, and transform the way you see, think, and shape the world around you. The path to enlightenment is geometric; let yours begin here.

 
 

Course Lessons

Average Lesson Rating:
4.3 / 5 Stars (Average Rating)
"Extraordinarily Helpful"
(1,407 votes)

Lesson 1. Foundations of Geometry and Their Practical Applications

Understanding geometry enhances problem-solving skills for both practical and academic purposes, across diverse areas like designing, construction, and scientific inquiry. This lesson provides foundational definitions of geometric figures, such as points and lines, which are essential for further study and applications. Additional lesson topics: Geometry Glossary 16 Total Points
  • Lesson 1 Video A
  • Lesson 1 Video B : How to Take an Exam
  • Lesson discussions: Reasons for Taking this Course
  • Complete: Lesson 1 Assignment
  • Assessment: Lesson 1 Geometry Terms and Motivation
  • Assessment: Lesson 1 Exercises

Lesson 2. Deductive Reasoning: A Deep Dive into Geometry

Exploring deductive reasoning in geometry, this lesson covers deriving conclusions from premises, using logical if-then statements, and conducting proofs by contradiction. Additionally, it discusses using arbitrary units for measurement and understanding the significance of dimensions such as length, area, and volume. 11 Total Points
  • Lesson 2 Video
  • Complete: Lesson 2 Activity
  • Assessment: Lesson 2 Geometric Reasoning and Measurement

Lesson 3. Angles and Parallel Lines in Geometry

In this lesson, angles are introduced and classified by size, demonstrating how intersecting lines can form multiple angles and highlighting the properties of vertical and supplementary pairs. Parallelism is defined through the interaction of angles when a transversal cuts across parallel lines, leading to the identification of corresponding angles. Additional lesson topics: Types of Angles 9 Total Points
  • Lesson 3 Video
  • Assessment: Lesson 3 Angles and Parallelism

Lesson 4. Decoding the Secrets of Triangles: Types and Properties

Triangles are three-sided polygons characterized by non-coincident, non-parallel lines, where the sum of the angles adds up to 180 degrees, which we proved through angle properties derived from parallel lines and transversals. This lesson covers various triangle types and introduces right triangles, their properties, and methods to calculate areas, preparing students to explore triangle congruence and similarity. Additional lesson topics: Triangle Practice Problems--Angles; Simplify Radicals; Triangle Practice Problems--Area 14 Total Points
  • Lesson 4 Video
  • Complete: Lesson 4 Activity
  • Assessment: Lesson 4 Triangles I: Properties of Triangles
  • Assessment: Lesson 4 Exercises

Lesson 5. Mastering Congruent Triangles: A Study of Geometric Similarities

The lesson elucidates criteria such as SSS that confirm triangle congruence, showing how certain side and angle pairings prove triangle identity. By concentrating on congruence, learners enhance their ability to pinpoint identical triangles amidst complex figures. 14 Total Points
  • Lesson 5 Video
  • Complete: Lesson 5 Activity
  • Assessment: Lesson 5 Triangles II: Congruent Triangles
  • Assessment: Lesson 5 Exercises

Lesson 6. Triangles and Transformation: Discovering Similarity

This lesson enriches students' understanding of triangle similarity, highlighting the use of transformations and three proportionality-based conditions. By utilizing transformations like dilation, students can prove triangle similarity, even when congruence is not present. Additional lesson topics: Similar triangles 7 Total Points
  • Lesson 6 Video
  • Assessment: Lesson 6 Triangles III: Similar Triangles

Lesson 7. Quadrilaterals Unlocked: From Basic Shapes to Calculating Areas

Lesson Summary 2: This lesson delves into quadrilaterals, explaining their basic properties and differentiating between subcategories like trapezoids and parallelograms based on parallel sides and angles. Utilizing the properties of triangles, students learn to compute areas of various quadrilateral types, reinforcing geometric understanding through formulas and examples. Additional lesson topics: Quadrilateral Overview 10 Total Points
  • Lesson 7 Video
  • Assessment: Lesson 7 Quadrilaterals

Lesson 8. Polygon Perimeters and Properties

Building on basic three- and four-sided figures, the lesson delves into the world of n-sided polygons, offering techniques for calculating perimeter and interior angles. Using subdivision, complex polygons can be broken down for easier analysis and understanding. 17 Total Points
  • Lesson 8 Video
  • Assessment: Lesson 8 Polygons
  • Assessment: Lesson 8 Exercises

Lesson 9. Understanding Circles: Essential Concepts and Calculations

Focusing on circles, this lesson distinguishes them from polygons by exploring equidistant points from a center, defining key elements such as radius and diameter, and utilizing degree measurements to understand arcs and sectors. It provides formulas for calculating circumference and area, introducing the crucial mathematical constant ?. 11 Total Points
  • Lesson 9 Video
  • Complete: Lesson 9 Activity
  • Assessment: Lesson 9 Circles

Lesson 10. Exploring the World of Composite Figures: An Analytical Journey

Composite figures, which are combinations of simpler shapes, require a methodical approach of division into basic parts to determine characteristics like area and perimeter. The lesson hones skills in breaking down complex shapes for analysis, making use of known geometric properties. Additional lesson topics: Composite Figures Video 10 Total Points
  • Lesson 10 Video
  • Assessment: Lesson 10 Composite Figures

Lesson 11. Pencil and Compass: The Art of Classical Constructions

With the use of a compass, straightedge, and pencil, this lesson guides students through classical geometric constructions, emphasizing the lasting relevance and precision of these fundamental techniques. As students engage with bisecting lines and angles, they gain a deep appreciation for the craftsmanship of geometry beyond modern computation. Additional lesson topics: Geometrical Construction 10 Total Points
  • Lesson 11 Video
  • Assessment: Lesson 11 Classical Construction

Lesson 12. Hands-On Geometry: Applying What You've Learned

This lesson introduces practical geometry applications by outlining problem-solving steps, using scenarios like calculating composite floor areas and solving practice exercises with diagrams and measurements. Emphasizing unit awareness and triangle congruence, it reinforces using geometric relationships to simplify real-world problems. Additional lesson topics: Geometry Word Problems 11 Total Points
  • Lesson 12 Video
  • Complete: Lesson 12 Activity
  • Assessment: Lesson 12 Practical Geometry Problems

Lesson 13. Parallelism and Perpendicularity Beyond Two Dimensions

Examining the intricacies of three-dimensional geometry, this lesson presents concepts like skew lines and multiple parallel planes that elevate the understanding of spatial relationships. Visual representation techniques and cross sections are key tools provided to facilitate the comprehension of 3D structures on 2D surfaces. Additional lesson topics: Solid Geometry 11 Total Points
  • Lesson 13 Video
  • Complete: Lesson 13 Activity
  • Assessment: Lesson 13 Three-Dimensional Geometry I

Lesson 14. Advanced Exploration of Polyhedra and 3D Shapes: Volume and Surface Analysis

Lesson Summary 3: Lesson 14 deepens the understanding of three-dimensional shapes by highlighting the measures of volume and surface area, focusing specifically on polyhedra, spheres, and cylinders. The lesson equips learners with tools to effectively compute and solve practice problems involving both standalone and composite geometric figures. Additional lesson topics: Volume of a Rectangular Prism Video 10 Total Points
  • Lesson 14 Video
  • Assessment: Lesson 14 Three-Dimensional Geometry II

Lesson 15. Introduction to Trigonometry: Understanding Angles and Sides

The lesson connects the intricate elements of trigonometry with geometry, using sine, cosine, and tangent to unravel the symmetrical mysteries of right triangles and their relation to circles. Mastery here equips you with a robust framework for solving diverse geometric problems, expanding your mathematical toolkit beyond basic formulas. 53 Total Points
  • Lesson 15 Video
  • Lesson discussions: What do you think about this course?; Program Evaluation Follow-up Survey (End of Course); Course Comments
  • Assessment: Lesson 15 Geometry and Trigonometry
  • Assessment: The Final Exam
214
Total Course Points
 

Learning Outcomes

By successfully completing this course, students will be able to:
  • Identify and describe fundamental geometric figures such as points, lines, rays, and planes by illustrating them accurately with examples.
  • Recognize the importance of geometry in daily life, academia, and professional settings by providing three examples of practical applications.
  • Define deductive reasoning and demonstrate deriving conclusions from given premises.
  • Explain the importance of units in geometric measurement and demonstrate using arbitrary units for measurement.
  • Recognize and construct a two-column proof for basic geometric problems.
  • Demonstrate understanding of angle relationships and properties when a transversal intersects two parallel lines.
  • Identify and calculate the measures of angles formed by intersecting lines using degree measurements.
  • Calculate the length of a side in a right triangle using the Pythagorean theorem.
  • Identify and classify triangles as equilateral, isosceles, or scalene based on side lengths and angles.
  • Demonstrate congruence between two triangles using the hypotenuse-leg (HL) condition in right triangles.
  • Recognize and justify the four conditions (SSS, SAS, ASA, AAS) for triangle congruence through geometric reasoning.
  • Prove the similarity of any two given triangles by applying the appropriate conditions such as angle-angle, side-side-side proportionality, or side-angle-side proportionality.
  • Demonstrate how to use geometric transformations to show two triangles are similar, including dilation and translation, within a structured problem-solving process.
  • Demonstrate mastery of lesson content at levels of 70% or higher.
 

Additional Course Information

Online CEU Certificate
  • Document Your Lifelong Learning Achievements
  • Earn an Official Certificate Documenting Course Hours and CEUs
  • Verify Your Certificate with a Unique Serial Number Online
  • View and Share Your Certificate Online or Download/Print as PDF
  • Display Your Certificate on Your Resume and Promote Your Achievements Using Social Media
Document Your CEUs on Your Resume
 
Course Title: Geometry 101: Beginner to Intermediate Level
Course Number: 9770452
Lessons Rating: 4.3 / 5 Stars (1,407 votes)
Languages: English - United States, Canada and other English speaking countries
Availability: This course is fully available online in all 50 states, including California, Texas, Florida, New York, Pennsylvania, Illinois, Ohio, and Georgia. It’s also offered in major English-speaking countries, such as the United Kingdom, Canada, Australia, and Ireland.
Last Updated: July 2024
CEU Value: 1.7 IACET CEUs (Continuing Education Units)
CE Accreditation: Universal Class, Inc. has been accredited as an Authorized Provider by the International Association for Continuing Education and Training (IACET).
Grading Policy: Earn a final grade of 70% or higher to receive an online/downloadable CEU Certification documenting CEUs earned.
Course Type: Self-Paced, Online Classes
Assessment Method: Lesson assignments and review exams
Instructor: April Cordry-Moore
Syllabus: View Syllabus

Student Testimonials

  • "Course was a bit difficult for me, instructor was available and helped me when I needed help!" -- Marcus M.
  • "This was a great course. I learned a lot about Geometry and am excited to use what I learned here in my high school. It was definitely better than some of the other Universal courses I took because this instructor, Mr. Clark, was more organized and thorough with his lessons, and it was easier to understand him than other university's instructors." -- Hannah Z.
  • "He was an excellent teacher...the lessons were very clear and easy to understand. I also like the 15 lesson layout." -- Rayna K.