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**Eligibility:** CTY-level or Advanced CTY-level math score required

**Prerequisites:** Successful 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. Students are also introduced to a dynamic software tool, GeoGebra, through projects that they create. Additionally, students are invited to participate and ask questions in an open Help Room guided by instructors.

Each student is assigned to a CTY instructor to help them during their course. Students can contact their instructors via email with any questions or concerns at any time. Live one-on-one online review sessions can be scheduled as well to prepare for the graded assessments, which include homework, chapter tests, and a cumulative midterm and final.

Instructors use virtual classroom software allowing video, voice, text, screen sharing, and whiteboard interaction. Students are strongly encouraged to work on the course at least 1 hour a day, 5 days a week (for a 6-month enrollment), and email their instructors at least once per week.

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

For a detailed list of topics, click the List of Topics tab.

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

Each week, all active students are invited to an open Geometry Help Room, which is led by a rotating staff of instructors. Students are encouraged to come with questions or just to meet other online students. Topics reviewed vary each week.

The Geometry Help Room meets each Wednesday from 7 – 8 p.m. ET.

Sample Video

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

**Zoom online virtual classroom**

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students who are unable to attend live sessions will need a computer with the Zoom desktop client installed to watch recorded meetings. The Zoom desktop client and Zoom Mobile App are both available for free download.

This course uses Respondus LockDown Browser proctoring software for designated assessments. LockDown Browser is a client application that is installed to a local computer. Visit the Respondus website for system requirements.

While Chromebook can be used to progress through the course, all exams must be completed on a PC or Mac.