High School

# Geometry/Geometry Honors

1.0 Credit
2 segments/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: 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]

### Competencies

##### 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.

### 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.

Open

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.

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

### Competencies

##### 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.

### Projects

Open

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:

*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.

### Competencies

##### 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.