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Advanced Geometry – Test: Unit 1 Outline 250 Points Thursday, September 22, 2011 I. - Terms / Definitions / Postulates / Naming Geometric Figures (see back of the sheet) Know the definitions (you will have to write out a definitions). Know how to name parts of figures, determine how many segments or angles are in a figure, and apply simple probability to a figure, etc. II. - Box Principle / Pigeonhole Principle Be able to identify the "boxes" and "pigeons" in a given problem Be able to explain how the Box Principle applies to a problem (See Problem 2 on WA #1) Be able to use the ideas of the Box Principle to solve problems. (How many people in a room at minimum to guarantee 13 people were born in the same month?) III. - Inductive Reasoning / Sequences Identify the next number in a sequence and provide an explanation for your choice Work with Arithmetic Sequences (constant add/subtract) and Geometric Sequences (constant multiply) Generate a rule for the nth term of a sequence (either a number or picture sequence) Know various techniques for finding "weird" an = ? [ Skeleton Tower, etc ] Know what Gauss did in order to add up a bunch of numbers and be able to show it (Watch for the twist like Problem 12 on the quiz!) IV. - Segments and Angles Know how to use the "Segment Addition Postulate" Know how to solve segment word problems (like #4 from the quiz) Know how to use the "Angle Addition Postulate" (watch for adding or subtracting expressions) Know how to solve for lengths of segments and measures of angles algebraically (Especially when systems of equations emerge – elimination) V. - 4 Interesting Points in Triangles / Constructions Know how to construct perpendicular bisectors and angle bisectors Incenter, Circumcenter, Centroid, Orthocenter: Know how to construct each (and the circles, if applicable) using a compass and straightedge Given a picture, be able to identify which point is illustrated Be able to construct the circle containing any given three noncollinear points Know the properties of the centroid - ~~~~~~~~~~~~~~~~~~~~~~~~~~~ NOTES ~~~~~~~~~~~~~~~~~~~~~~~~~~~ - Calculators, compasses, protractors, and rulers are all required for the exam. This is a major grade ... prepare accordingly! You will have the entire block; take responsibility for your performance! A. Terms to Know... (Be able to define or describe the following... watch for important items you must include in your definition.) Point Perpendicular Lines Line Parallel Lines Plane Perpendicular Bisector Segment Angle Bisector Ray Incenter Angle Circumcenter Collinear Points Median of a Triangle Coplanar Points Centroid Congruent Segments Altitude of a Triangle Congruent Angles Orthocenter Complementary Angles Postulate Supplementary Angles Inductive Reasoning Adjacent Angles Sequence Linear Pair of Angles Arithmetic Sequence Right Angle Geometric Sequence Acute Angle Midpoint of a Segment Obtuse Angle B. Postulates Know the 5 postulates on the "Building Blocks of Geometry" sheet Segment Addition Postulate Angle Addition Postulate C. Naming Figures / Geometry Symbols Know how to name figures appropriately Know the symbol for congruence (angle, segment, line, ray, plane, etc) D. Look through your notes Written Assignment #1, and Quiz #1; hopefully you've put in time daily; be confident and prepared! E. Last minute questions? Find me before 8:00 AM Thursday. Once 8:00 AM has arrived, I will not give an overview of any topic. (Don't come to class expecting a five minute review before the test.)