1.0 Credit
2 segments/32-36 weeks
Open

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.

### Competencies

##### 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.

##### Geometric Constructions

Students will demonstrate an understanding of geometric constructions by creating constructions, explaining the logic underlying constructions, and creating regular polygons using construction techniques.

##### ransformations 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.

##### Circles

Students will demonstrate an understanding of circles by describing circle properties, solving circle theorems, and applying circle applications.

##### 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.

### 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

### Course Materials

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.