1 Revised 11/00 NVCC COLLEGE-WIDE COURSE CONTENT SUMMARY MTH 006 - DEVELOPMENTAL GEOMETRY (2 CR.) COURSE DESCRIPTION Covers topics in Euclidean geometry including similarity and congruency, plane and solid figures, right triangles, parallel and perpendicular lines, constructions, and applications. Develops the mathematical proficiency necessary for selected curriculum entrance. Credits not applicable toward graduation. Lecture 2 hours per week. GENERAL COURSE PURPOSE The purpose of this course is to (a) develop competency in the basic geometry skills necessary to succeed in 100-level math courses and (b) develop skills in the oral and written use of geometric terminology. ENTRY LEVEL COMPETENCIES Prerequisites are a satisfactory score on an appropriate proficiency examination and Algebra I or equivalent. COURSE OBJECTIVES Upon completion of this course, the student will be able to: A. use congruency and similarity theorems to prove triangles congruent or similar B. solve for unknown components of triangles and quadrilaterals using similarity theorems and the Pythagorean theorem C. compute areas and volumes of simple geometric figures D. identify components of circles E. use properties of parallel and perpendicular lines to explain the characteristics of quadrilaterals MAJOR TOPICS TO BE INCLUDED A. Undefined terms: point, line, and plane B. Basic axioms C. Angles 1. types 2. congruency D. Triangles 1. types 2. congruency 3. right triangles 4. median, altitude, angle bisector 5. similarity 6. Pythagorean Theorem 7. 30 - 60 - 90 triangle and 45 - 45 - 90 triangle2 E. Parallelism 1. parallel postulate 2. determining parallelism 3. properties of parallel lines F. Basic constructions G. Quadrilaterals - definition of: 1. parallelogram 2. rhombus 3. rectangle 4. square 5. trapezoid H. Areas - formulas and applications: 1. rectangle 2. parallelogram 3. triangle 4. trapezoid I. Circles 1. parts: radius, diameter, arc, chord, secant, tangent, central angles, inscribed angles 2. area and circumferences J. Volumes - formulas and applications 1. rectangular solid 2. cylinder 3. cone 4. sphere EXTRA TOPICS (optional) A. Mathematical logic: direct and indirect proofs B, Transformations: reflections, translations, rotations C. Coordinate geometry D. Geometric