Geometry – Homeschool

Course Description

Geometry is a time-honored branch of mathematics rooted in the teachings of Pythagoras, Euclid, and Archimedes. This course offers a comprehensive introduction to Euclidean geometry, including foundational concepts such as definitions, postulates, and theorems. Students will explore line and angle relationships, parallel lines, congruent and similar triangles, polygons, circles and arcs, and the Pythagorean Theorem.

The course also covers measurement of perimeter, area, and volume in both two and three dimensions, and introduces advanced topics such as coordinate geometry, spatial geometry, basic constructions, and introductory trigonometry.


General Information

Most Cool Math Guy (formerly Chalk Dust) video programs are based on textbooks published by the College Division of a leading educational publisher. These textbooks—used for Basic Math, Prealgebra, Algebra 1, and Algebra 2—align well with high school-level content and are frequently adopted in college non-credit prep courses.

Geometry, however, is an exception. The textbook used for this course contains more advanced vocabulary and content than is typically found in standard high school texts. At the time of video production, it was the only suitable geometry textbook available.

To better align the course with traditional high school expectations:

  • Some chapters and selected sections are omitted

  • Custom worksheets are included to reinforce key topics and simulate a high school curriculum more accurately


How the Course Works

  1. The student begins by watching a video lesson (typically 30–50 minutes long), then starts the corresponding textbook assignment.

  2. The student pauses at the end of their scheduled math time for the day.

  3. On the following day, the student continues the assignment. A third day may be needed to complete the work—and that’s okay.

  4. After finishing a chapter (or midway through), the student completes a practice test, followed the next day by the chapter test. Parents should administer both.

  5. The process repeats with the next section until the course is completed.


When Help Is Needed

Support is available in several forms when students or parents encounter difficulties:

  1. Re-watch the video lesson for clarification

  2. Refer to similar examples in the textbook

  3. Review the problem in the solutions manual

  4. Submit a question through the Cool Math Guy website—responses typically arrive within 24 hours


Sample Videos from this Course

Section 1.4 Angles and Their Relationships
Section 3.1 Congruent Triangles
Section 4.2 The Parallelogram and Kite
Section 6.3 Line and Segment Relationships in the Circle

Table of Contents

  • 1.1  Sets, Statements and Reasoning
  • 1.2  Informal Geometry and Measurement
  • 1.3  Early Definitions and Postulates
  • 1.4  Angles and Their Relationships
  • 1.5  Introduction to Geometric Proof
  • 1.6  Relationships: Perpendicular Lines
  • 1.7  The Formal Proof of a Theorem
  • 2.1  The Parallel Postulate and Special Angles
  • 2.2  Indirect Proof
  • 2.3  Proving Lines Parallel
  • 2.4  The Angles of a Triangle
  • 2.5  Convex Polygons
  • 2.6  Symmetry and Transformations
  • 3.1  Congruent Triangles
  • 3.2  Corresponding Parts of Congruent Triangles
  • 3.3  Isosceles Triangles
  • 3.4  Basic Constructions Justified
  • 3.5  Inequalities in a Triangle
  • 4.1  Properties of a Parallelogram
  • 4.2  The Parallelogram and Kite
  • 4.3  The Rectangle, Square, and Rhombus
  • 4.4  The Trapezoid
  • 5.1  Ratios, Rates, and Proportions
  • 5.2  Similar Polygons
  • 5.3  Proving Triangles Similar
  • 5.4  The Pythagorean Theorem
  • 5.5  Special Right Triangles
  • 5.6  Segments Divided Proportionately
  • 6.1  Circles and Related Segments and Angles
  • 6.2  More Angle Measures in the Circle
  • 6.3  Line and Segment Relationships in the Circle
  • 6.4  Some Constructions and Inequalities for the Circle
  • 7.1  Locus of Points
  • 7.2  Concurrence of Lines
  • 7.3  More About Regular Polygons
  • 8.1  Area and Initial Postulates
  • 8.2  Perimeter and Area of Polygons
  • 8.3  Regular Polygons and Area
  • 8.4  Circumference and Area of a Circle
  • 8.5  More Area Relationships in the Circle
  • 9.1  Prisms, Area, and Volume
  • 9.2  Pyramids, Area, and Volume
  • 9.3  Cylinders and Cones
  • 9.4  Polyhedrons and Spheres
  • 10.1  The Rectangular Coordinate System
  • 10.2  Graphs of Linear Equations and Slope
  • 10.3  Preparing to do Analytic Proofs
  • 10.4  Analytic Proofs
  • 10.5  Equations of Lines
  • 11.1  The Sine Ratio and Applications
  • 11.2  The Cosine Ratio and Applications
  • 11.3  The Tangent Ratio and Other Ratios
  • 11.4  Applications with Acute Triangles

Supporting Parents

We understand that questions can come up, especially in the beginning. Personal support is available via text, email, or phone. We’re here to help both parents and students every step of the way.


Course Materials

Textbook Recommendations

Below are the recommended textbook and solutions manual for this course. Both correlate directly with the video instruction. Used copies can be found online at affordable prices.

Note: The textbook includes answers to selected homework problems. The solutions manual provides step-by-step explanations and is helpful, though not essential.

Textbook Recommendation
Elementary Geometry, 6th Edition by Alexander

 

Practice Tests, Tests, and Answer Keys

All assignments and testing materials are available to subscribers through a password-protected link.


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