Virtual Classroom @ Your Library Geometry

Welcome to the Abilene Public Library’s Virtual Classroom.  This space will offer a new place for youth, teens, and adults to learn more about a variety of topics, with new content added regularly.

For each class, we'll share background information, educational videos, lesson plans, resources available for continued learning and more. Plus, we’ll offer a link to a test we’d appreciate if you completed to show what you learned!

Euclid of Alexandria (lived c. 300 BCE)

EuclidEuclid of Alexandria lived circa 300 BCE.  He systematized mathematics and geometry derived earlier from the Greeks and the Near East.  He wrote the Elements which is a set of books on MathematicsIt is noted that he also wrote perhaps a dozen other titles, but most of those are lost to time.

Palmer, N. (2015, October 23). Euclid. Ancient History Encyclopedia. Retrieved from
Oldes surviving Euclids Elements
Euclid's Influence
For approximately 2000 years, Euclid's works entitled the Elements were considered a perfect example of correct reasoning. More than a thousand editions of his work have been published, making it the most popular book ever written outside of the Bible.
Palmer, N. (2015, October 23). Euclid. Ancient History Encyclopedia. Retrieved from
The Elements

Euclid did not come up with all of the ideas in The Elements. Rather he gathered knowledge and wrote a textbook of known ideas of the time.  It does not cover all known information, but focuses on definitions, postulates and axioms.  He demonstrated that geometry was proven by logical steps from axioms and postulates.  Euclid also included some of his original discoveries like infinitely prime numbers.  His book is divided into sections of Chapters 1-6 featuring Plane Geometry.  Chapters 7-10 describe Arithmetic and number theory.  In chapters 11-13 he explores Solid Geometry.  Four other books are still in existence.  They are entitled Data, Division of Figures, Phenomena and Optics.
English elements
First English version of The Elements. To read a full text version of this ancient book visit this site and download the book.


Geometry on Khan Academy: We are surrounded by space. And that space contains lots of things. And these things have shapes. In geometry we are concerned with the nature of these shapes, how we define them, and what they teach us about the world at large--from math to architecture to biology to astronomy (and everything in between). Learning geometry is about more than just taking your medicine ("It's good for you!"), it's at the core of everything that exists--including you. Having said all that, some of the specific topics we'll cover include angles, intersecting lines, right triangles, perimeter, area, volume, circles, triangles, quadrilaterals, analytic geometry, and geometric constructions.
This lesson introduces the concept of Euclidean geometry and how it is used in the real world today. This lesson also traces the history of geometry.


Euclidean Geometry is the Geometry of flat space.It is based on the work of Euclid who was the father of Geometry.  He proposed 5 postulates or axioms that are the foundation of this mathematical branch of Geometry.   The 5 postulates are...

1. It is possible to draw a straight line from any point to any point. 

2. If you have a straight line it is possible to extend in any direction to infinity.

3.It is possible to draw a circle given any center and a radius 

4.All right angles are equal (congruent).

5.If you have two straight lines, and a third line crossing them, and the sum of the interior angle measure of the two lines is less than two 90 degrees, then if you extend the lines, they will eventually cross on that side.

Geometry lies at the root of all drawing, so it's good to know a little about it. This is the first video in a series which will explain the basics of Euclid's Elements of Geometry. Don't be scared - It's quite fun!  The drawings and script are the basis of the book and ebook, Euclid, The Man Who Invented Geometry

  1. Resources
  2. Lesson Plans
  3. Test Your Knowledge
Geometry Resources

Geometry Games for Kids
Wikipedia contributors. (2020, December 4). Geometry. In Wikipedia, The Free Encyclopedia. Retrieved 18:55, December 7, 2020
Geometry Lesson for Kids: History & Facts  (need and account)
Geometry with DK
Geometry - Definition with Examples
High School Geometry
Painless geometryStudents discover relationships that exist between parallel and perpendicular lines; analyze the characteristics of distinct shapes such as circles, quadrilaterals, and triangles; and learn how geometric principles can solve real-world problems.

Perfect Math For Students Who Are Math Challenged.  Lessons are presented in a format that everyone can understand.  Each Lesson flows smoothly and logically to the next.  Each lesson is short, concise, and to the point.  Lots of examples with step-by -step solutions.  Each lesson includes valuable Helpful Hints section.  Review is built into each lesson. Students will retain what they have learned!  Each lesson includes Problem Solving. This ensures that students will learn to apply their math skills to real-life situations.  Includes free access to video tutorials. Just go to and click on the Videos button. Passwords are in red print.

Get in shape

Provides an introduction to two-dimensional and three-dimensional shapes.

Reading Level: 4-7.

With scrumptious-looking photos, easy recipes, and a variety of pies to bake or just ogle, this book provides a fun and memorable approach to thinking and learning about circles, polygons, angles, parallel and perpendicular lines, tessellation, symmetry, area, volume, and more. This book will leave the reader with a taste for geometry!
geometry is as easy as pie
Dr. Math
Dr. Math presents more geometry : learning geometry is easy! just ask Dr. Math!  Students just like you have been turning to Dr. Math for years asking questions about math problems, and the math doctors at The Math Forum have helped them find the answers with lots of clear explanations and helpful hints. Now, with Dr. Math Presents More Geometry, you'll learn just what it takes to succeed in this subject. You'll find the answers to dozens of real questions from students in a typical geometry class. You'll also find plenty of hints and shortcuts for using coordinate geometry, finding angle relationships, and working with circles. Pretty soon, everything from the Pythagorean theorem to logic and proofs will make more sense. Plus, you'll get plenty of tips for working with all kinds of real-life problems.