Optimal thought and optimal fitness through reason, logic, science, passion, and wisdom.
Gold Academy: Private and Corporate Training
Geometry Preview/Review, Session 1

Geometry Preview/Review, Session 1

Schedule: We will meet for two weeks, five days a week, 1.5 hours per day. (15 hours total.)

Format: An intro course to prep for a semester of geometry, with lecture to cover concepts, and lots of class interaction and individual practice. We will learn concepts and practice them to attain the mastery we can in a short time, in preparation for a longer, graded course during a school year. No grading; homework is optional.

Cost: $250 per person for a group class of 4 or more students; $935 for one-on-one tutoring.

Payment options: Payments can be made via PayPal, Venmo, Zelle, cash, or check.

Materials: A graphing calculator like a TI-84, TI-89, HP Prime, or Casio is recommended. No text. We’ll use free worksheets on the Internet for homework and supplements.

For more details or to schedule a class, contact Michael by email at michaelgold@goldams.com or by phone at 281-770-2276.

Class Description.

Get ready for high school geometry by getting a head start and giving yourself more time to assimilate concepts and techniques that some students find difficult. Or review some important geometric concepts and ideas (like that of proof). Good for SAT/ACT prep. Good for getting ready for calculus. Good for making sure you learned some essentials of high school geometry.

We will learn how proofs work, take a look at what geometry studies, get some geometry concepts under our belts, and develop some strategies for learning geometry. We cannot cover everything in here that is covered in a year-long geometry course, of course, but we can learn some geometric concepts and some geometric methods.

Which we should do, as geometry has had a profound impact for the better on our culture and world. We will dig into some of that impact so we know why geometry is important, so we know exactly how it helps in thought and in life, and so we know what logic and proof really are. The point of education is to develop the ability to reason independently, the point is not do destroy it, so I teach multidisciplinary thinking, understanding, and logic as I work. I do not do the blind memorization, the compartmentalized “thinking,” or the homework-problems-in-isolation thing. I do not teach math-in-a-box, I teach what real people in the real world need to know to survive and thrive (and get good grades with understanding, not parroting).

We will have some lecture, some interactive work, and some independent work that we will check in class. Everyone will get a chance to ask and answer questions, get feedback, and check their understanding.

You will get some class notes posted everyday on Outschool (you will need to take some of your own notes!), some optional extra reading for understanding, and lots of optional practice work. All classes on Outschool are recorded, so you can watch ones you might have to miss and watch class over again to take notes or review.

Note: this course is preparation for a high school geometry course. It is preparation for a semester 1 (and some semester 2).


  1. Geometry, what it is and why it is important
  2. Derivation of some area and volume formulas
  3. Parallel lines and angles around a transversal
  4. Theorems about triangles and congruent triangles
  5. Quadrilaterals and diagonals
  6. Proof, what it is and why it matters
    (And nore (e.g., internal and external angles in a polygon; induction vs. deductions; similarity) if time permits.)

Tentative schedule (subject to change to fit the class needs and interests). We will meet for two weeks, five days per week, 1.5 hours per day.

Week 1
Day 1
-what geometry is and why it is important; what you should aim to get out of it; how to study it; the idea of proof
-derivation of some the common area formulas (so we understand, not merely memorize)
-area exercises
Day 2
-derivation of other common area formulas
-derivation of some volume formulas (so, again, we understand, not merely memorize)
-area and volume exercises
Day 3
-basic terms of geometry; naming geometric figures
-parallel lines, transversals, and angles
-proof that the angles of a triangle actually do add to 180º
-the exterior angle theorem
Day 4
-types of triangles; their characteristics
-definiton congruence; congruent triangles
-triangle congruence theorems and practice proofs
Day 5
-finish topics

Week 2
Day 1
-triangle congruence theorems and practice proofs
Day 2
-triangle congruence theorems and practice proofs
Day 3
-types of quadrilaterals; diagonals of quadrilaterals
-theorems about quadrilaterals (parallelograms, trapezoids, rectangle, rhombus)
Day 4
-theorems about quadrilaterals (parallelograms, trapezoids, rectangle, rhombus)
Day 5
-finish topics

Taking this particular course over would also help retain the material in the long run — we need it for algebra 2, precalculus, calculus, the SAT, the ACT, and for many situations in real life.

I agree with Martin Luther King, Jr., and teach accordingly: “Education must also train one for quick, resolute and effective thinking. To think incisively and to think for one’s self is very difficult. We are prone to let our mental life become invaded by legions of half truths, prejudices, and propaganda. At this point, I often wonder whether or not education is fulfilling its purpose. A great majority of the so-called educated people do not think logically and scientifically. Even the press, the classroom, the platform, and the pulpit in many instances do not give us objective and unbiased truths. To save man from the morass of propaganda, in my opinion, is one of the chief aims of education. Education must enable one to sift and weigh evidence, to discern the true from the false, the real from the unreal, and the facts from the fiction.” –Martin Luther King, Jr. (From MLK’s 1947 article “The Purpose of Education,” published in the Morehouse College campus newspaper The Maroon Tiger.

Learning Goals.
To learn what geometry is about and why it is important.
To learn basic and important geometric concepts.
To learn how to do proofs.
To learn how human knowledge is developed.

“Never before was my son as motivated and interested in a course. It was a delight to see and fun to hear him share about the lessons without prodding 😄”
–Paula L., parent, “High School Geometry, Semester 1,” 2 Jan 2022

“This class helped my son prepare for 9th grade Geometry Honors. He felt the teacher was very prepared, extremely knowledgeable, worked at a good pace for understanding and was thorough. There was time for questions and help if needed. He enjoyed taking this class.”
–Laura S., parent, “Summer Geometry Preview/Review, Session 1,” 22 Aug 2021

“Great overview of what geometry class will be like in the upcoming school year. It teaches you how to think about geometry, and the importance of logic and systematic thinking in general.”
–Gita S., parent “Summer Geometry Preview/Review, Session 1,” 28 Jun 2020

Michael Gold’s “Summer Geometry Preview/Review” was a in-depth yet efficient way (8-classes over a two-week period @ 1.5 hours per class) to get a preview of what to expect in the fall. My daughter wants to stay sharp over the summer (around the fun and relaxation that all kids need) and the structure of a class that meets live is the only option for us. Also, the class was comprised of like-minded students and a nice group of kids.

We first came to know Mr. Gold through his “Logic Essentials: How to Think Well” class. I highly recommend this class because logic and deductive reasoning are the cornerstones of thinking well. We need our kids to flag poor arguments and discern the truth. Unless you are attending an elite prep school, I don’t know where you would find exposure to a class like this. I am so grateful that Mr. Gold makes this class offering available. So when I shared Mr. Gold’s Geometry offering with my daughter, she wanted to sign up knowing he is a wonderful teacher.

What was most telling – my daughter never forgot about the class date or time. I know Mr. Gold is engaging because if I walked past her room, she was never distracted. He connected with kids on all fronts using lecture, illustrating problems on the board and showing YouTube videos. He has a warm personality, inflection in his voice and good sense humor. After each class ended, my daughter wanted to show me her notes and explain a problem set she learned. Also, I received a detailed email from Mr. Gold outlining everything that was covered in each class, along with links to videos, books, geometry worksheets and more. I also appreciate that homework was optional – your child can leisurely gain exposure or go all out on mastering the subject matter – there’s no pressure.

Michael Gold has high standards for teaching and truly cares about his students. My family joins his long list of five star reviews because he’s that good. My daughter and I highly recommend Mr. Gold’s ‘Summer Geometry Preview/Review’ and ‘Logic Essentials: How to Think Well’. We enthusiastically encourage you to sign up for any class he teaches!
–Mary B, parent, “Summer Geometry Preview/Review, Session 1,” 19 Aug 2020