## Essentials Geometry A

### Enrollment Message:

By enrolling students in this class you are agreeing to following terms of use: Enroll only students who have previously failed the equivalent course or who are enrolled in an approved alternative education program. Provide time in the studentâ€™s regular school schedule for completion of this course. These courses permit students to test out of content and therefore are not NCAA eligible. If you are enrolling a student athlete for Credit Recovery purposes, we recommend our full-length Plus courses. Total course points may vary per student based on the items students test out of. The total points in the course may vary per student based upon the number of lessons which each individual demonstrates mastery through scores earned on lesson pre-tests. Students will be exempted from the points possible on a lesson quiz associated with successfully passing a related lesson pre-test.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.
**Prerequisites:** Algebra 1

**Course Objectives:** Upon completion of this course, students will be able to...

- Explain differences between a postulate and a theorem
- Demonstrate how tools like a compass and a straightedge help to construct congruent segments, segment bisectors, angles, and angle bisectors
- Demonstrate and explain how to construct parallel and perpendicular lines and a regular polygon inside a circle
- Explain how translation, reflections, and rotations are represented as functions and the relationship between each and rigid motion
- Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motion
- Prove that vertical angles are congruent and that a point on a perpendicular bisector is equidistant from the endpoints of the segments it intersects
- Prove theorems behind parallel lines cut by a bisector
- Prove each of the following: triangle sum, isosceles triangle, converse of the isosceles triangle, midsegment of a triangle, and concurrency of medians
- Prove each of the following properties of a parallelogram: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, if the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram, and rectangles are parallelograms with congruent diagonals
- Demonstrate how dilations and functions are related and how to dilate figures on the coordinate plane.
- Explain if polygons are similar and the relationships between corresponding sides and angles of similar polygons.
- Explain and utilize the Triangle Proportionality Theorem, The Converse of Triangle Proportionality Theorem, Pythagorean Theorem, and The Converse of the Pythagorean Theorem.

**Course Outline:**

Module 1

Module 2

Module 3

Module 4

Module 5

**Resources Included:** Online lesson instruction and activities, opportunities to engage with a certified, online instructor and classmates, when appropriate, and online assessments to measure student performance of course objectives and readiness for subsequent academic pursuits.

**Additional Costs:** Graphing calculator or online graphing calculator

**Scoring System: **Michigan Virtual does not assign letter grades, grant credit for courses, nor issue diplomas. A final score out of total points earned will be submitted to your school mentor for conversion to their own letter grading system. Total course points may vary per student based on the items students test out of. The total points in the course may vary per student based upon the number of lessons which each individual demonstrates mastery through scores earned on lesson pre-tests. Students will be exempted from the points possible on a lesson quiz associated with successfully passing a related lesson pre-test.

**Time Commitment:** Semester sessions are 18-weeks long: Students must be able to spend 1 or more hours per day in the course to be successful. Summer sessions are 10 weeks long: Students must be able to spend a minimum of 2 or more hours per day, or about 90 hours during the summer, for the student to be successful in any course. Trimester sessions are 12-weeks long: Students must be able to spend 1.5 or more hours per day in the course to be successful.

**Technology Requirements: ** Students will require a computer device with headphones, a microphone, webcam, up-to-date Chrome Web Browser, and access to YouTube.

Please review the Michigan Virtual Technology Requirements: https://michiganvirtual.org/about/support/knowledge-base/technical-requirements/

Lightweight devices such as Apple iPads, Google Chromebooks, and tablets have limited support for Java which still appears in a small percentage of FLVS courses. FLVS has worked to de-Flash its courses. Students may need extra work-around steps or alternate browsers to engage with some portions of select courses or may be required to utilize text-alternatives for some interactive objects. FLVS recommends students have a Windows or Mac based computer available to complete coursework in the event that your selected mobile device does not meet the needs of the course. Fully supported Operating Systems for FLVS courses include Windows (7 or higher), Mac OS X (10.8 or higher), and MacOS (10.12 or higher). Supported Browsers include the most recent versions of Microsoft Edge, Mozilla Firefox, Google Chrome, and Apple Safari on devices that support Java and HTML5. Browsers need to be up to date, and some FLVS courses may require installation or enabling of the following Plug-ins: JavaScript enabled, Cookies enabled, Java installed. https://www.flvs.net/student-resources/system-requirements

**Instructor Support System: **For technical issues within your course, contact the Customer Care Center by email at [email protected] or by phone at (888) 889-2840.

**Instructor Contact Expectations: **Students can use email or the private message system within the Student Learning Portal to access highly qualified teachers when they need instructor assistance. Students will also receive feedback on their work inside the learning management system. The Instructor Info area of their course may describe additional communication options.

**Academic Support Available: **In addition to access to a highly qualified, Michigan certified teacher, students have access to academic videos and outside resources verified by Michigan Virtual. For technical issues within the course, students can contact the Michigan Virtual Customer Care by email at [email protected] or by phone at (888) 889-2840.

**Required Assessment: **Online assessments consist of formative and summative assessments represented by computer-graded multiple choice, instructor-graded writing assignments including hands-on projects, model building and other forms of authentic assessments.

**Technical Skills Needed:** No special skills are required beyond being able to operate a computer and use word processing software.

**Additional Information:** This course permits students to test out of content and therefore are not NCAA eligible. If you are enrolling a student athlete for Credit Recovery purposes, we recommend our full-length Plus courses.