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 geometric truths. From these truths he deduced all the postulates and theorems you will study in this course. Elements 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 have 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:
- determine coordinates of points located on segments.
- use the formulas for distance, slope, and midpoint and derive them.
- verify whether lines are parallel, perpendicular, or neither using formulas
- determine the equation of a line that passes through a particular point and is parallel or perpendicular to a given line
- transform figures in a plane by dilating, translating, reflecting, and rotating them.
- describe a transformation in words and in coordinate notation
- identify a sequence of transformations that will move one object onto another.
- distinguish and identify objects that have reflectional and rotational symmetry.
- identify whether a term is undefined, a definition, a postulate, a theorem, or a conjecture.
- determine whether a conditional statement is true or false; and if it is true, give a reasonable counterexample.
- identify, compare, and contrast a conditional statement with its converse, inverse, and contrapositive.
- contrast Euclidean and spherical geometries through examining the concepts of parallel lines and the sum of the angles in a triangle.
- prove various theorems about angles and apply these theorems to solve problems.
- prove triangles are congruent using triangle congruence theorems.
- apply the definition of triangle congruence to identify congruent sides and angles.
- verify theorems about triangles, such as the Pythagorean Theorem, and apply these theorems 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 1: Elements of Plane Geometry
Topic 2: Reasoning and Proofs
Topic 3: Transforming Figures
Topic 4: Triangles and Geometric Constructions