Geometry is the study of points, lines, surfaces, shapes, 3-dimensional solids, and the relationships that exist between them. Fundamental to the study of these objects is the formation of logical arguments that allow someone to make a claim based on previously known truths. In 300 BCE Euclid, commonly known as the “Father of Geometry” wrote a book titled Elements which begins with a few basic agreed upon truths from which he deduced all the postulates and theorems you will study in this course. This book was so influential that it was used as a primary source of mathematics teaching for more than two thousand years.
In this course you will learn to use both ancient technologies (like a compass and straight edge) and modern technologies (like graphing utilities and video tutorials) to develop skills that are used on a daily basis by carpenters, lawyers, and artists.
If you’ve ever wondered why bees use hexagons to build their hives, how to construct a logical argument that will be irrefutable, or how to create more interesting artwork using geometry, then this course will give you a new perspective on the world around us!
Upon completing this course you will be able to:
- recognize various types of quadrilaterals and prove which one it is based on given conditions.
- identify similar figures and when sides and angles are proportionate or congruent.
- apply the Angle-Angle criterion and apply it to solve problems.
- prove the triangle proportionality and use it to solve problems.
- identify and apply the geometric mean in right triangles.
- use trigonometry to find side lengths and angle measures in right triangles.
- recognize special right triangles and apply their properties to solve problems.
- identify 3-dimensional solids like prisms, pyramids, cylinders, cones, and spheres and describe the shapes of their cross sections.
- determine how a change in the linear dimension of these solids will affect the surface area or volume.
- find the area of regular polygons and composite figures.
- identify and use the formulas for surface area and volume of 3-dimensional figures to solve real world problems.
- apply properties of circles including radii, chords, tangents, secants, circumference, sector area, and arc length to solve problems.
- describe the relationship between an angle’s measure in radians, arc length, and the radius of the circle.
- identify and use the equations of circles.
- develop and use strategies to solve problems of permutations and combinations.
- use an area model to determine probabilities.
- identify independent events and dependent events and calculate their probabilities.
- apply conditional probability and independence to solve problems.
Required Course Materials
- Math Journal – In the form of a small composition notebook, a spiral notebook, or loose-leaf paper kept in a binder.
- Pencil or Pen – In order to do well in the course, you must take notes, sketch diagrams and graphs, and solve problems when instructed to do so.
- Purchasing a TI 84 plus, a TI 83 or similar is recommended.
- Compass, Straight Edge, and Protractor
- Internet Access
- Adobe Reader
Note: This course does not require a textbook.
Each semester contains 4 units and one final exam that must be taken in person.
Each Unit contains:
- 4–5 lessons. Each lesson includes some or all of the following components: Engage, Explore, Explain, Elaborate, and Evaluate.
- Self-assessments to help you check your own understanding of the material covered in each lesson. You must complete these assessments in order to advance in the course.
- 3 graded assignments
The final examination is comprehensive; it covers the material from all units. To pass the course, you must receive a grade of 70 percent or better. You can apply to take the Final Exam after 100 percent of your graded assignments have been submitted, and at least 70 percent have been graded and returned to you.
Time Allowed: 3 hours
Materials Allowed: #2 pencils, graphing calculator
Topic 5: Similar Figures
Topic 6: Polygons and Circles
Topic 7: Three-dimensional Figures
Topic 8: Circle Theorems and Probability