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Estimated Completion Time

2 segments/32-36 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: content varies depending on course version. For currently enrolled students, please refer to the syllabus located in the course information area for curriculum specifics.

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



Credits 1


  • Circles
    Students will demonstrate an understanding of circles by reasoning with and applying theorems about circles.
  • Congruence
    Students will demonstrate an understanding of congruence by proving geometric theorems and creating logical arguments about various geometric figures such as lines, triangles and parallelograms.
  • Expressing Geometric Properties with Equations
    Students will demonstrate an understanding of geometric properties by using coordinates and applying algebraic models to express and prove geometric relationships.
  • Right Triangles and Trigonometry
    Students will demonstrate an understanding of right triangles by reasoning to solve right triangles using various techniques including Pythagorean Theorem, trigonometric ratios, and special right triangle properties.
  • Rigid Motion
    Students will demonstrate an understanding of rigid motions by analyzing various types of rigid motions and congruence in terms of rigid motion.
  • Similarity
    Students will demonstrate an understanding of similarity through working with dilations, similar polygons, similar triangles, and proofs of similarity and using the concepts of congruence and similarity to solve real-world problems.
  • Solid Geometry
    Students will demonstrate an understanding of solid geometry by calculating volume of various solid figures, problem solving, and visualizing the relationship between two and three dimensional figures.


Algebra 1 Segment 1, or the following Algebra Competencies: Linear Equations, Linear Inequalities, Graphs and Linear Functions.

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.