Download 250 Points

Advanced Geometry – Test: Unit 1 Outline
250 Points
Thursday, September 22, 2011
I.
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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.
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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.
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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.
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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.
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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
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~~~~~~~~~~~~~~~~~~~~~~~~~~~ NOTES ~~~~~~~~~~~~~~~~~~~~~~~~~~~
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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.)