Introduction Mathematics 22G Geometry: Second Semester

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1 Geometry: Second Semester Overview of the Course This geometry course is designed to help you develop problem-solving skills for real-world problems. Geometry uses mathematics to examine the relationship between points, lines, and planes, with other concepts such as solids, polygons, angles, polyhedrons and circles. Geometry also nurtures your ability to think logically about situations through the use of proofs. Algebra is a very valuable tool in geometry, so the successful completion of an Algebra course is required before starting this course, as is the successful completion of first semester Geometry. This second semester course will focus on the many wonders of quadrilaterals, including differentiating based on known facts; the amazing circle and how it can be used to help solve problems; polygons and finding areas of polygons; and polyhedrons, including drawing nets, finding surface areas, and finding volumes. We will again be using proofs and constructions throughout this semester, just as we did first semester. Prerequisites You must have successfully completed first and second semester Algebra I and first semester Geometry before beginning this course. Required Materials You will need a scientific calculator, compass, straightedge and protractor for Math 22G. You will also need access to a scanner for submitting Part 2 of the lesson assignments. If you do not have Adobe Reader installed on your computer, get a free download from Adobe.com You will need it for downloading PDF worksheets. Course Organization and Outline The course will be divided into eight study lessons and two examinations. The eight lessons will focus on geometry concepts and will include assignments consisting of multiple choice and open-ended questions. The two examinations will focus on four lessons each and will consist only of open-ended questions. i

2 Lesson 1: Quadrilaterals Part 1 This lesson will cover angles of polygons, diagonals, interior and exterior angle sums, parallelograms, rectangles, rhombi and squares. Lesson 2: Quadrilaterals Part 2 This lesson will cover tests for parallelograms, constructions of quadrilaterals, trapezoids, and coordinate proofs with quadrilaterals. Lesson 3: Transformations This lesson will cover reflections, translations, rotations and dilations. Lesson 4: Circles This lesson will cover the basics of circles, including angles, arcs, chords, inscribed angles, tangents, secants, special segments in a circle, and the equation of a circle. Lesson 5: Midterm Examination In this lesson you will receive tips for preparing for and taking the midterm exam covering the material in lessons 1-4. Lesson 6: Area of Polygons (Part 1) This lesson will cover finding the area of parallelograms, triangles, trapezoids, and rhombi. Lesson 7: Area of Polygons (Part 2) and Circles This lesson will cover finding the area of regular polygons, irregular polygons and circles and geometric probability. Lesson 8: Surface Area of Polyhedra This lesson will cover three-dimensional figures, nets, and finding the surface area of prisms, cylinders, pyramids, cones, and spheres. Lesson 9: Volume of Polyhedra This lesson will cover finding the volume of prisms, cylinders, pyramids, cones, and spheres, and congruent and similar solids. Lesson 10: Final Examination In this lesson you will receive tips for preparing for and taking the midterm exam covering the material in lessons 6-9. ii

3 Grading Introduction Each of your lessons will be graded for accuracy and you are expected to show all work on the open-ended questions for full credit. The examinations are worth 60 percent and the two-part lesson assignments are worth 40 percent of your course grade. Each lesson assignment will contain 20 questions consisting of Part 1: 10 multiple-choice questions worth 1 point apiece Part 2: 10 open-ended questions worth 2 points apiece for a total of 30 points per lesson. There will be 240 points total for the eight lessons. The examinations will be worth 180 points each for a total of 360 points. There are 600 total points possible for the course. The grading scale will be as follows: points = 97.0 to 100.0% = A points = 93.0 to 96.9% = A points = 90.0 to 92.9% = A minus points = 87.0 to 89.9% = B points = 83.0 to 86.9% = B points = 80.0 to 82.9% = B minus points = 77.0 to 79.9% = C points = 73.0 to 76.9% = C points = 70.0 to 72.9% = C minus points = 67.0 to 69.9% = D points = 63.0 to 66.9% = D points = 60.0 to 62.9% = D minus 359 points or less = 59.0% or less = F Completing the Lessons Each study lesson (lessons 1 4 and 6 9), is organized in the following manner. You will first encounter several objectives for the lesson. Look these over carefully. The objectives list the skills we hope you will gain as you complete the discussions and exercises in the lesson. An overview will give you a sense of what to expect from the lesson, and what you will need to know and do. Next will be the discussion for the lesson. It will provide the kinds of explanation you would generally get in a classroom lecture, so it is important for you to read the discussion carefully. At the end of each discussion section, you will find a practice sheet, where you can check your understanding of the material and practice answering the types of questions you ll see on the iii

4 exams. You should complete the practice sheets as you work through the discussion sections and before you submit your assignment. However, the practice sheets are just learning tools: they will not count toward your grade. Although you should <em>not</em> submit them to your instructor, if you have questions about the practice sheets, don t hesitate to ask your instructor when you send in your assignment. Finally, you will need to complete the two-part assignment. Part 1 is a set of 10 multiple choice questions, which you will complete in Oncourse Tests & Surveys. Part 2 is a set of 10 openended questions, which you will download from Oncourse Assignments. Print the document and neatly write your answers on it. Use extra paper if necessary. Then scan your pages and save the file as a PDF that you will submit to your instructor. Remember, if your instructor cannot read an answer, it will not be counted. Each lesson also includes access to reference materials: a glossary of terms; a document of all theorems, postulates, and corollaries introduced throughout the course; and flash cards with which you can review vocabulary as you prepare for exams. Completing the Exams Lesson 5 and 10 are designed to prepare you for the course examinations. The following is the procedure for these lessons. 1. Using the form provided with lesson 5 and lesson 10 on the syllabus, request the exam. Each exam will be sent to an official who will supervise you as you take the test. Please direct all questions involved with requesting or receiving the exam to the Independent Study Program office. Your instructor does not issue the exams. 2. You may request the exams after you have completed the lessons leading up to each exam. Since the exams test your knowledge of the topics from the preceding lessons, you should wait to take the exams until you have had the opportunity to look over your graded assignments. The best way to learn is to understand your mistakes. 3. Rework the questions from the lessons prior to the exam for better understanding. Questions on the exams will be similar in format and content to the questions from the assignments. Pay particular attention to your instructor s comments and spend time to correct your mistakes on the assignments so you do not repeat those on the exams. 4. You must have an exam average (the sum of your two exams divided by two) of at least a 60% to receive credit for this course, regardless of your assignment average. iv

5 A Note About Web Browsers Introduction This course is designed to work best in the Mozilla Firefox browser. Many of the math symbols throughout this course may not work correctly in other browsers. Make sure you are using the latest version of Firefox, available as a free download at US/firefox/new/. v