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Honors Geometry (NCAA Approved)

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

Prerequisites: Successful completion of Algebra I or equivalent

Course Format: Session Based. See calendar for session dates and application deadlines

Course Length: 30 weeks

Recommended School Credit: One academic year

Student Expectations: Students are strongly encouraged to work at least 1 hour a day, 5 days a week

Course Code: GEOY

Course Description


This proof-based geometry course, covers concepts typically offered in a full-year honors geometry course. To supplement the lessons in the textbook, 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.

This course has synchronous virtual class meetings and students may also schedule one-on-one virtual meetings directly with the instructor to answer questions or concerns. The instructor will schedule meeting dates/times at the start of the course. Meetings will be recorded for students who are unable to attend due to scheduling conflicts. Additionally, students are invited to participate and ask questions in an open Help Room guided by instructors.

In this course, participation in forums and synchronous online virtual sessions are required as part of the final grade. Discussion forums are located within the course where students will be required to respond to a given prompt and then comment on responses by other students. Online sessions, led by a CTY instructor, are held in a virtual classroom, which allows for video, voice, text, screen sharing, and whiteboard interaction.

Students can contact their instructors via email with 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 exams, and a cumulative midterm and final.

Terms and Conditions

Virtual classrooms, and student activities in the classroom, may be recorded and added to the course as an ongoing asset for all class students to review. Students may be invited to interact in CTY community spaces that include students and instructors and potentially specially invited guests that are not enrolled in their course. Student contributions (e.g., projects, forum posts, etc.) may remain in the course after the student completes the course. These artifacts may be preserved to showcase student work or to continue important conversations.

Topics include:

  • 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.

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Materials Needed

There are no required materials for this course.

List of Topics

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

Chapter 1: Basics of Geometry

  • Points, Lines, and Planes
  • Measuring and Constructing Segments
  • Using Midpoint and Distance Formulas
  • Perimeter and Area in the Coordinate Plane
  • Measuring and Constructing Angles
  • Describing Pairs of Angles

Chapter 2: Reasoning and Proofs

  • Conditional Statements
  • Inductive and Deductive Reasoning
  • Postulates and Diagrams
  • Algebraic Reasoning
  • Proving Statements about Segments and Angles
  • Proving Geometric Relationships

Chapter 3: Parallel and Perpendicular Lines

  • Pairs of Lines and Angles
  • Parallel Lines and Transversals
  • Proofs with Parallel Lines
  • Proofs with Perpendicular Lines
  • Equations of Parallel and Perpendicular Lines

Chapter 4: Transformations

  • Translations
  • Reflections
  • Rotations
  • Congruence and Transformations
  • Dilations
  • Similarity and Transformations

Chapter 5: Congruent Triangles

  • Angles of Triangles
  • Congruent Polygons
  • Proving Triangle Congruence by SAS
  • Equilateral and Isosceles Triangles
  • Proving Triangle Congruence by SSS
  • Proving Triangle Congruence by ASA and AAS
  • Using Congruent Triangles
  • Coordinate Proofs

Chapter 6: Relationships Within Triangles

  • Perpendicular and Angle Bisectors
  • Bisectors of Triangles
  • Medians and Altitudes of Triangles
  • The Triangle Midsegment Theorem
  • Indirect Proof and Inequalities in One Triangle
  • Inequalities in Two Triangles

Chapter 7: Quadrilaterals and Other Polygons

  • Angles of Polygons
  • Properties of Parallelograms
  • Proving that a Quadrilateral is a Parallelogram
  • Properties of Special Parallelograms
  • Properties of Trapezoids and Kites

Chapter 8: Similarity

  • Similar Polygons
  • Proving Triangle Similarity by AA
  • Proving Triangle Similarity by SSS and SAS
  • Proportionality Theorems

Chapter 9: Right Triangles and Trigonometry

  • The Pythagorean Theorem
  • Special Right Triangles
  • Similar Right Triangles
  • The Tangent Ratio
  • The Sine and Cosine Ratios
  • Solving Right Triangles
  • Law of Sines and Law of Cosines

Chapter 10: Circles

  • Lines and Segments that Intersect Circles
  • Finding Arc Measures
  • Using Chords
  • Inscribed Angles and Polygons
  • Angle Relationships in Circles
  • Segment Relationships in Circles
  • Circles in the Coordinate Plane
  • Locus and Constructions

Chapter 11: Circumference, Area, and Volume

  • Circumference and Arc Length
  • Areas of Circles and Sectors
  • Areas of Polygons
  • Three-Dimensional Figures
  • Volumes of Prisms and Cylinders
  • Volumes of Pyramids
  • Surface Areas and Volumes of Cones
  • Surface Area and Volumes of Spheres

(Optional) Chapter 12: Probability

  • Sample Spaces and Probability
  • Independent and Dependent Events
  • Two-Way Tables and Probability
  • Probability of Disjoint and Overlapping Events
  • Permutations and Combinations
  • Binomial Distributions

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Geometry Help Room

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 every Wednesday and Thursday from 7–8 p.m. ET.

Technical Requirements

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 which can be used for instructor-student communication if the student has any questions about the course or curriculum. The classroom works on standard computers with the Zoom desktop client and also tablets or handhelds that support the Zoom Mobile app. Students will need a computer with the Zoom desktop client installed to watch any 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.