Course Title: Plane Geometry CP Course Length: One Year Credits: 10 credits Grades: 8-12 Morgan Hill Unified School District Course Outline Course Goals Students will be able to apply to properties of logic when developing mathematical arguments. Students will be able to apply concepts developed through reasoning to real world situations. Students will be able to interpret and apply spatial relationships. Students will be able to relate algebraic and geometric concepts. Texts and Supplemental Instructional Materials Larson, Ron, Boswell, Laurie, Kanold, Timothy D., Stiff, Lee, Geometry. Boston: McDougal Littell, 2007. Text resources Teacher made resources Manipulatives Scientific Calculator Course Objectives by Essential Standards Standard 1: Students will be able to identify and give examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. Standard 2: Students will be able to write geometric proofs, including proofs by contradiction. Standard 3: Students will be able to construct and judge the validity of a logical argument. Standard 4: Students will be able to prove basic theorems involving congruence and similarity. Standard 5: Students will be able to prove triangles are congruent or similar and be able to use the concept of corresponding parts of congruent triangles. Standard 6: Students will be able to use the Triangle Inequality Theorem.
2 Standard 7: Students will be able to prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. Standard 8: Students will be able to derive, and solve problems involving perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. Standard 9: Students will be able to compute volumes of prisms, pyramids, cylinders, cones, and spheres. Standard 10: Students will be able to compute areas of polygons including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. Standard 11: Students will be able to determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. Standard 12: Students will be able to find and use measures of sides, interior and exterior angles of triangles and polygons to classify figures and solve problems. Standard 13: Students will be able to prove relationships between angles in polygons using properties of complementary, supplementary, vertical, and exterior angles. Standard 14: Students will be able to prove the Pythagorean Theorem. Standard 15: Students will be able to use the Pythagorean Theorem to determine distance and find missing lengths of sides of right triangles. Standard 16: Students will be able to perform basic constructions with straightedge and compass such as angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. Standard 17: Students will be able to prove theorems using coordinate geometry, including the midpoint of a line segment, distance formula, and various forms of equations of lines and circles.
3 Standard 18: Students will be able to apply the basic trigonometric functions defined by the angles of a right triangle. They will be able to use the elementary relationships between them, (e.g. tan(x)= sin(x)/cos(x)). Standard 19: Students will be able to use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. Standard 20: Students will be able to use angle and side relationships in problems with special right triangles such as 30-60-90 triangles and 45-45-90 triangles. Standard 21: Students will be able to prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. Standard 22: Students will be able to illustrate the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. Outline of Course Major Units Elements of Geometry Points, Lines, Planes Subsets of a line Introduction to deductive reasoning Proof in two column form Angles and Perpendicular Lines Angles, and their measures Introduction to Theorems, Corollaries Concerning Angles Parallel Lines and Planes Sufficient and Necessary Conditions for Parallel Lines Applications of Parallel Lines to Polygons Theorems and proofs for Parallel Lines Congruent Triangles Concept of Correspondence Between Two Triangles Methods of Proving Congruent Triangles Corresponding Parts of Congruent Triangles Use of Corresponding Parts of Congruent Triangles for Extended Proofs Introduction of Auxiliary Lines
4 Applications of Congruent Triangles Parallelograms (Necessary and Sufficient Conditions for Parallelograms) Other Quadrilaterals (Rectangles, Rhombi, Squares, and Trapezoids) Triangle Inequalities Similar and Regular Polygons Concept of Proportionality Properties of a Proportion Definition of a Similar Polygon (Similar Triangles and Proofs Involving Similar Triangles Definition of a Regular Polygon Area of Regular Polygons Angle Rules for Polygons Right Triangles Pythagorean Theorem and its Applications Special Right Triangles Geometric Mean Trigonometric Ratios and basic applications Circles Tangents, Arcs, and Chords Angles formed by segments in relation to a Circle Segments, lines, and rays in relation to a Circle Circumference and Area of Circles Area and Volume of Solids including Spheres, Cones, Prisms, Cylinders, & Pyramids. Coordinate Geometry Cartesian Plane Measurement of Segments in a Cartesian Plane Equations of a Line and its properties Slope of Line Methods of Instruction Investigations/Explorations Group/Individual Activities Collaborative Learning (pairs/groups) Lecture/Discussion Use of Manipulatives/games Building Content Vocabulary Writing Assignments/Portfolio Audio Visual Materials Guest Speakers/Field Trips Notebook
5 Assessment methods and/or tools Assessment methods include formative assessment, which will promote learning throughout the course or summative assessments, such as benchmarks, final exams, which document student progress toward meeting standards. These methods include: Homework and periodic checks of student work. Textbook and teacher generated tests and quizzes. Assessments periodically must include formal proofs. A variety of selected responses, which may include, but not limited to multiple-choice, true/false, matching, and short answer fill-in items. Personal communication may include, but limited to, teacher/student conference and interviews, teacher observation, classroom discussions, oral examinations, and journals and logs. Peer activities may be used as an assessment for appropriate topics Essay assessments evaluating student s knowledge, reasoning, and skills. Performance, e.g. student projects, performances, debates, and presentations.