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Geometry - The Basics & Beyond

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What you'll learn


  • Master the vocabulary needed for success in a Geometry class

  • Describe a polygon, give examples and non-examples

  • List the basic parts of a circle

  • Calculate the area and perimeter of rectangles and triangles

  • Describe the concepts of perimeter, area, and volume

  • Calculate the volume of a right prism (given the area of the base)

  • Categorize angles, triangles, and undefined terms by sight

  • Name angles, rays, lines, and segments using symbolic shorthand


  • Apply the concepts of precise definitions and counter-examples

  • Construct items such as perpendicular segment bisectors using both electronic tools and paper, compass, straight-edge and-pencil

  • Define rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

  • Determine the image produce by a series of transformations

  • Use transformation to prove SSS, SAS, ASA, and AAS

  • Determine the series of transformations required to create a particular image (given a pre-image)

  • Use transformations to prove congruency of shapes

  • Use two-column proofs to prove theorems about triangles, quadrilaterals, and parallel lines

About this Course

The demand for my basics course was so high, I decided to expand it and charge a small fee for the extra time and effort for pulling these lectures and external resources together. The first expansion includes explanation and practice for about a quarter of the Common Core standards. Specifically it includes all the “Congruence” standards which encompasses the new focus on transformations as well as a lot of traditional two column proofs. Eventually I hope to make it to make it through all of the Common Core standards - either here or in other courses.

THE BASICS - The original Course:

Having taught Geometry for almost a decade, I’ve learned that one of the biggest challenges is simply the vocabulary. This first (and original) section is a very broad overview of Geometry and the language that it uses. If you’ve never heard this vocabulary, this will introduce it. If you have, this will reinforce it and put it into context.

Said another way there are a few different kinds of students who would benefit from this section:

  • Those who are about to take Geometry
  • Those who are taking Geometry and want a review or another perspective
  • Those who are curious as to the overall nature of Geometry but not wanting to take time for an entire course

Some of the vocabulary and concepts discussed are used in every day conversations, whereas others are specialized and not usually found in everyday conversation (I’m looking at you, hypotenuse!). Some of these terms SHOULD be familiar while others will not be. The course also includes a lot outside resources to practice as well as Udemy-style quizzes.

There’s an old joke about what you remember from a college course five years after you’ve taken it. For Economics, it’s supply and demand. For Chemistry, it’s the periodic table is the organization of the elements. For English Composition, it’s always start with an outline. This limited course is along those same lines: it will give you the general feeling for topics in Geometry without many of the details.

The first section could be watched in one sitting if you don’t do any of the exercises. A better way to take it would be to target one day for a week to watch one video (less than 10 minutes) and then spending 20 minutes after each lecture to explore the additional material that’s included.

SECTION 2 - Common Core Congruence Standards

First, a word about Common Core. IF you live in a state that has rigorous Mathematical Standards, Common Core is simply a nationalized version of a variation of what has been taught over the last 20 years. It stresses some new topics and ignores some traditional stuff, but it’s simply a road map for a GIANT TOPIC. In 180 school days, only so much can be learned about any given field - these standards attempt to point out what’s important and what’s not: Both in general and related to what will be on State/National assessment tests.

There are 13 standards related to “Congruence” in the New Common Core and this section explains (at varying levels of depth in it’s first iteration) all of them. I attacked this first because it had transformations in it and it was the one topic I knew I would have to do a fair amount of research on before I could teach it.

This section is primarily for students:

  • Interested in learning more about transformations and why they have become a new item of importance
  • Need more and different examples of two column proofs and strategies for solving these.