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Estimated Completion Time

2 segments/36 weeks


One day in 2580 B.C.E., a very serious architect stood in a dusty desert with a set of plans. His plans called for creating a structure 480 feet tall, with a square base and triangular sides, using stone blocks weighing two tons each. The Pharaoh wanted the job done right. The better this architect understood geometry, the better his chances were for staying alive.

Geometry is everywhere, not just in pyramids. Engineers use geometry to build highways and bridges. Artists use geometry to create perspective in their paintings, and mapmakers help travelers find things using the points located on a geometric grid. Throughout this course, students travel a mathematical highway illuminated by spatial relationships, reasoning, connections, and problem-solving.

Note: Exact content varies depending on the course version. For currently enrolled students, please refer to the syllabus located in the course information area for curriculum specifics.

This offering may only be completed through courses or projects and meets mathematics graduation requirements. Select either the “Courses” or “Projects” buttons for a more detailed description of these options. If you wish to take Algebra 1 and Geometry concurrently, please contact [email protected]

Course Requirements

Besides engaging students in challenging curriculum, VLACS guides students to reflect on their learning and to evaluate their progress through a variety of assessments. Assessments can be in the form of self-checks, practice lessons, multiple choice questions, projects, oral assessments and discussions. Instructors evaluate progress and provide interventions through the variety of assessments built into a course, as well as through contact with the student in other venues.

Major Topics and Concepts

Segment I

Module 01 Basics of Geometry

  • Basics of Geometry
  • Basic Constructions
  • Constructing with Parallel and Perpendicular Lines
  • Constructions with Technology
  • Introduction to Proofs


Module 02 Transformations and Congruence

  • Translations
  • Reflections
  • Rotations
  • Rigid Motion and Congruence


Module 03 Proofs of Theorems

  • Line and Angle Proofs
  • Triangle Proofs
  • Parallelogram Proofs


Module 04 Dilations and Similarity

  • Dilations
  • Similar Polygons
  • Similar Triangles


Module 05 Triangle Similarity Proofs

  • Triangle Congruence and Similarity
  • Applications of Congruence and Similarity


Segment 2

Module 06 Coordinate Geometry

  • Using the Coordinates
  • Slope
  • Coordinate Applications


Module 07 Right Triangles and Trigonometry

  • 07.01 Solving Right Triangles
  • 07.02 Trigonometric Ratios
  • 07.04 Applying Trigonometric Ratios


Module 08 Volume and Figures

  • Formulas
  • Applications of Volume
  • Density
  • 3-D Figures


Module 09 Circles

  • Properties of a Circle
  • Inscribed and Circumscribed Circles
  • Applications of Circles




Each competency will be addressed through a project that is based on a real-life career task. Here are the careers you will explore: Gemologist, Textile Designer, Transportation Planner, Irrigation Design Engineer, Package Designer, and Land Surveyor.



Estimated Completion Time

32-36 weeks


Please review the competency statements to learn the major topics and concepts covered in this offering.



Projects allow students to demonstrate their understanding of concepts and skills by completing a job-related task. The assignment might be to create a mural, a package design, a speech, a film review, or a movie set – you name it! These creative projects are about applying your learning acquired through in-depth research to real-world career tasks.



Experiences allow you to explore a career field you’re curious about while mastering competencies for school credit. Through experiential learning, you will learn skills and apply these skills to tasks you would complete as part of a career, rather than completing traditional assessments like essays or tests. During your experience, you’ll work with a professional in the field to support your learning. You’ll earn a badge for your accomplishments, which you can share on social media and higher education platforms, or with colleges, potential employers, peers, and/or colleagues to display your qualifications.

Here’s how experiences work:

  1. Each competency you work on is addressed through a separate deliverable predetermined by you and your instructor.
  2. Guided learning for each module consists of research and/or work with a professional in the field. Your instructor will coach you through this process.
  3. Each module culminates in a final demonstration of understanding, which includes a deliverable and a discussion-based assessment with your instructor.

Here’s an example:

Let’s say you’re curious about a career in healthcare. You decide you’d like to learn about this career area, make a professional connection, earn a badge and earn competencies for your 9th grade English requirement. While enrolled in English 1 Experiences, you conduct research to better understand language and structure in writing. Then, you work with an Occupational Therapist who helps you apply this understanding to the creation of an informational video. The video aims to advise the family members of patients regarding adaptive equipment and accommodations to help them support their family members as they go about their daily tasks. You’ve earned the Language and Structure in Writing competency! (This is just one example of the many ways experiences can bridge competencies to careers.)

*A parent/guardian permission form and background check of the outside expert are required for students to work with outside experts without parental supervision.


*Please have an idea for an outside expert in mind prior to enrollment or consult with our counseling department by emailing [email protected] prior to enrollment for support identifying one.

Credits 1


  • Transformations and Congruence
    Students will demonstrate an understanding of transformations and congruence by describing transformations of rigid motion, describing congruence by rigid motion, solving geometric theorems, and creating logical arguments.
  • Dilations and Similarity
    Students will demonstrate an understanding of dilations and similarity by explaining dilation of a geometric figure and dilation rules, describing similar triangles, and solving proofs and real-world problems involving congruence and similarity.
  • Coordinate Geometry
    Students will demonstrate an understanding of coordinate geometry by comparing geometric properties, proving geometric relationships, and describing algebraic models.
  • Right Triangles and Trigonometry
    Students will demonstrate an understanding of right triangles and trigonometry by explaining the Pythagorean Theorem, solving problems using trigonometric ratios, and comparing special right triangle properties.
  • Volume and Figures
    Students will demonstrate an understanding of volume and figures by explaining calculations for volume, explaining calculations for area, explaining calculations for density, and analyzing two and three dimensional figures.
  • Circles
    Students will demonstrate an understanding of circles by describing circle properties, solving circle theorems, and applying circle applications.


Algebra 1 Segment 1 OR completion of the following Algebra Competencies: Linear Equations, Linear Inequalities, Graphs, and Linear Functions.


Course: To complete the honors version of this offering, you must discuss this with your instructor during your welcome call. Projects: Honors credit is awarded by earning "Exceeds" on all rubric assessments.

Attend a virtual open house

We offer regular online open house webinars where VLACS staff members provide parents and students with an overview of our programs and answer questions about online learning.