/ CTYOnline / Courses / Mathematics

**Prerequisites:** Qualifying math score and completion of Algebra I or equivalent

**Course Format:** Individually Paced

**Course Length:** Typically 6 months

**Recommended School Credit:** One academic year

**Course Code:** GEO

Description

This proof-based geometry course, based on a popular classic textbook, covers concepts typically offered in a full-year honors geometry course. To supplement the lessons in the text book, videos, online interactives, assessments and projects provide students an opportunity to develop mathematical reasoning, critical thinking skills, and problem solving techniques to investigate and explore geometry. Additionally, students are introduced to a dynamic software tool, GeoGebra, through projects that they create.

The textbook must be purchased separately by the student.

- Deductive and inductive reasoning
- Direct and indirect proof
- Parallel lines and planes
- Congruence and similarity
- Polygons
- Perimeter, area, and volume
- Right triangles
- Circles
- Coordinate geometry
- Transformations and symmetry
- Constructions and Loci

There is a textbook purchase required for this course:

*Geometry*, 2000 edition by Jurgensen, Brown, & Jurgensen; McDougal Litell. ISBN: 0395977274

A compass is required in addition to the textbook.

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

- A Game and Some Geometry
- Points, Lines, and Planes
- Segments, Rays, and Distance
- Angles
- Postulates and Theorems Relating Points, Lines and Planes

- If-Then Statements; Converses
- Properties from Algebra
- Proving Theorems
- Special Pairs of Angles
- Perpendicular Lines
- Planning a Proof
- Flowchart and Paragraph Proofs

- Definitions
- Properties of Parallel Lines
- Proving Lines Parallel
- Angles of a Triangle
- Angles of a Polygon
- Inductive Reasoning

- Congruent Figures
- Some Ways to Prove Triangles are Congruent
- Using Congruent Triangles
- Isosceles Triangle Theorems
- Other Methods of Proving Triangles Congruent
- Using more than One Pair of Congruent Triangles
- Medians, Altitudes, and Perpendicular Bisectors

- Properties of Parallelograms
- Ways to Prove that Quadrilaterals are Parallelograms
- Theorems Involving Parallel Lines
- Special Parallelograms
- Trapezoids

- Inequalities
- Inverses and Contrapositives
- Indirect Proof
- Inequalities for One Triangle
- Inequalities for Two Triangles

- Ratio and Proportion
- Properties of Proportions
- Similar Polygons
- A Postulate for Similar Triangles
- Theorems for Similar Triangles
- Proportional Lengths

- Similarity in Right Triangles
- The Pythagorean Theorem
- The Converse of the Pythagorean Theorem
- Special Right Triangles
- The Tangent Ratio
- The Sine and Cosine Ratios
- Applications of Right Triangle Trigonometry
- Law of Sines and Law of Cosines

- Basic Terms
- Tangents
- Arcs and Central Angles
- Arcs and Chords
- Inscribed Angles
- Other Angles
- Circles and Lengths of Segments

- What Construction Means
- Perpendiculars and Parallels
- Concurrent Lines
- Circles
- Special Segments
- The Meaning of Locus
- Locus Problems
- Locus and Construction

- Areas of Rectangles
- Areas of Parallelograms, Triangles, and Rhombuses
- Areas of Trapezoids
- Areas of Regular Polygons
- Circumferences and Areas of Circles
- Arc Lengths and Areas of Sectors
- Ratios of Areas
- Geometric Probability

- Prisms
- Pyramids
- Cylinders and Cones
- Spheres
- Areas and Volume of Similar Solids

- The Distance Formula
- Slope of a Line
- Parallel and Perpendicular Lines
- Vectors
- The Midpoint Formula
- Graphing Linear Equations
- Writing Linear Equations
- Organizing Coordinate Proofs
- Coordinate Geometry Proofs

- Mappings and Functions
- Reflections
- Translations and Glide Reflections
- Rotations
- Dilations
- Composites of Mappings
- Inverses and the Identity
- Symmetry in the Plane and in Space

Sample Video

Sample GeoGebra Interactive

CTY*Online* courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course uses an online classroom for individual or group discussions with the instructor. The classroom works on standard computers with the Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile app.