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Math 484 Geometry for High School Teachers (Summer 2012) Teacher: Dr. Frances Gulick (office: MTH2101, email: [email protected], phone: 301 405 5154, office hours: right after class for a reasonable amount of time) Text: College Geometry Using the Geometer's Sketchpad, 1st Edition, Reynolds and Fenton, Wiley Publishing, 2012 or College Geometry, 1st Edition, with Geometer’s Sketchpad v5 Set by Barbara Reynolds, Nov. 2011. Dates: June 26-July 26, Tuesdays and Thursdays from 9 am to 1:30 pm. Objective. The objective of this course is to provide a solid foundation for in-service teachers in neutral and Euclidean geometry and given them an introduction to non-Euclidean geometry through the Lénart sphere and the Poincaré disk model for hyperbolic geometry as well as through the theory. In addition, teachers will gain experience in working with Geometers Sketchpad so that they can use it in the classroom both as a presentation tool and as an exploration tool for the students. The expectations of this course are consistent with the expectations of 400-level mathematics courses. The expectation is that we will cover Chapters 1-4, 6, 8, and 11 in College Geometry. There will be supplementary material, including an exploration with the Lénart sphere. Topics Axioms for Plane Geometry and immediate consequences Existence and incidence Distance and angle measure Plane separation SAS congruence Proof Writing proofs Indirect proof What is needed in a definition? Neutral geometry Triangle Congruence theorems Triangle inequalities Alternate Interior Angle Theorem Saccheri-Legendre Theorem Euclidean Parallel Postulate and equivalent statements Quadrilaterals Neutral constructions Euclidean Geometry Basic theorems with the parallel postulate Parallel Projection Theorem Similarity theorems Dividing a line segment into n congruent pieces Concurrent lines (medians, angle bisectors, altitudes, perpendicular bisectors) Ceva's Theorem, Menelaus' Theorem Area Postulates (Neutral and Euclidean) Decomposition and finding formulas Circles Angles and circles Inscribed and circumscribed polygons Circles and triangles, Euler line Lénart Sphere Intro to spherical geometry Sum of angles in triangle Failure of Incidence axioms No parallel lines Transformational Geometry Translations, rotations, reflections Isometries and congruence Dilations and similarity Inversion in a circle Analytic form Hyperbolic Geometry Some basic properties Poincaré Disk Model COURSE GRADE: The course grade will be based on homework and worksheets(100 points), Sketchpad activities (100 points) and two exams – a take-home midterm exam (100 points) and an in-class, closed-book final exam (150 points). You may work with others on your homework but what you turn in should be in your own words and mathematics (not copied from anyone else or any other source). Homework is due at the beginning of class. Sketchpad activities will be submitted via email. You may turn in one late assignment with no penalty if it is received within a week of the due date. Worksheet solutions are due on the same day they are done in class. This course operates under the Honor Code of the University of Maryland.