Radnor High School Course Syllabus Seminar Geometry 0429 I. Course Description This course is a challenging, rigorous, proof-based approach to Geometry. Students in Seminar Geometry analyze geometric figures using deductive reasoning, make conjectures and formulate hypotheses, draw conclusions and make connections with other mathematical concepts, and model situations geometrically as a problem solving strategy. Algebraic and geometric skills are integrated throughout the curriculum. II. Materials & Equipment Geometry for Enjoyment and Challenge; McDougal, Littell; 1991 Non-graphing, scientific calculator Geometer, compass, and straight edge Three – Ring Binder Notebook Water-Based Overhead Marker III. Course Goals & Objectives To develop the ability to think mathematically. To enhance problem solving ability. To use technology appropriately. To present a mathematical model of the physical world. To provide experience in solving geometry problems by deductive methods, direct or indirect. To supplement the basics of plane geometry with a foundation in space geometry, coordinate geometry and transformational geometry. To see the interrelationship of geometry to other fields of mathematics and relevant life situations. To challenge and utilize the inquisitive and logical minds of the accelerated math students. To foster specific problem solving strategies in an overall problem solving approach to mathematics. IV. Course Topics (Summary Outline) I. INTRODUCTION TO GEOMETRY Introductory Terminology Measurement of Segments and Angles Collinearity, Betweenness, and Assumptions Beginning Proofs Division of Segments and Angles Paragraph Proofs Deductive Structure Statements of Logic Probability Revised 05/17/2011 II. BASIC CONCEPTS AND PROOFS Perpendicularity Complementary and Supplementary Angles Drawing Conclusions Congruent Supplements and Complements Addition and Subtraction Properties Multiplication and Division Properties Transitive and Substitution Properties Vertical Angles III. CONGRUENT TRIANGLES Congruent Figures Methods to Prove Triangles Congruent CPCTC and beyond Circles Overlapping Triangles Types of Triangles Angle –Side Theorems IV. LINES IN THE PLANE Detours and Midpoints The Case of the Missing Diagram A Right-Angle Theorem The Equidistance Theorems Introduction to Parallel Lines Slope V. PARALLEL LINES AND RELATED FIGURES Indirect Proof Proving That Lines Are Parallel Congruent Angles Associated with Parallel Lines Four-Sided Polygons Properties of Quadrilaterals Proving That a Quadrilateral is a Parallelogram Proving That Figures Are Special Quadrilaterals VI. LINES AND PLANES IN SPACE Relating Lines to Planes Perpendicularity of a Line and a Plane Basic Facts about Parallel Planes VII. POLYGONS Triangle Application Theorems Two Proof- Oriented Triangle Theorems Formulas Involving Polygons Regular Polygons VIII. SIMILAR POLYGONS Ratio and Proportion Similarity Proving Triangles Similar Congruence and Proportions in Similar Triangles Three Theorems Involving Proportions Revised 05/17/2011 IX. THE PYTHAGOREAN THEOREM Review of Radicals and Quadratic Equations Introduction to Circles Altitude-on-Hypotenuse Theorems Pythagorean Theorem The Distance Formula Pythagorean Triples Special Right Triangles The Pythagorean Theorem and Space Figures Right Triangle Trigonometry X. CIRCLES The Circle Congruent Chords Arcs of a Circle Secants and Tangents Angles Related to a Circle Inscribed and Circumscribed Polygons The Power Theorems Circumference and Arc Length XI. AREA Area of Parallelograms, Squares, Rectangles and Triangles The Area of a Trapezoid Area of Kites and Related Figures Area of Regular Polygons Areas of Circles, Sectors, and Segments Ratios of Areas Hero’s and Brahmagupta’s Formulas XII. SURFACE AREA AND VOLUME Surface Areas of Prisms Surface Area of Pyramids Surface Areas of Circular Solids Volumes of Prisms and Cylinders Volumes of Pyramids and Cones Volumes of Spheres Ratios of Volumes of Similar Solids Continued on the next page: XIII. COORDINATE GEOMETRY EXTENDED Graphing Equations Equations of Lines Systems of Equations Graphing Inequalities Three-Dimensional Graphing and Reflections Equations of a Circle Coordinate-Geometry Practice XIV. LOCUS AND CONSTRUCTIONS Locus Compound Locus (if time permits) The Concurrence Theorems Basic Constructions Applications of the Basic Constructions Triangle Constructions XV. INEQUALITIES Number Properties Inequalities in a Triangle The Hinge Theorems XVI. ENRICHMANT TOPICS (Independent study for students participating in math team, and/or mathematics competitions.) The Point-Line Distance Formula Two Other Useful Formulas Stewart’s Theorem Ptolemy’s Theorem Mass Points Inradius and Circumradius Formulas Formulas for You to Develop Note: Algebra Reviews will also be assigned on a regular basis throughout the year in order for the students to maintain and extend their knowledge of Algebra. V. Assignments & Grading Assignment sheets will be distributed periodically throughout the school year. Homework will be assigned on a daily basis. Grades will be based on quizzes and tests. In addition, teachers may use homework, group activities, and/or projects for grading purposes. All students will take departmental midyear and final exams. The Radnor High School grading system and scale will be used to determine letter grades. Revised 05/17/2011