chapter 1
DESCRIPTION
Chapter 1. Reasoning in Geometry. Section 1-1. Patterns and inductive reasoning. Inductive Reasoning. When you make a conclusion based on a pattern of examples or past events. Conjecture. A conclusion that you reach based on inductive reasoning. Counterexample. - PowerPoint PPT PresentationTRANSCRIPT
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REASONING IN GEOMETRY
Chapter 1
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PATTERNS AND INDUCTIVE REASONING
Section 1-1
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Inductive Reasoning
When you make a conclusion based on a pattern of examples or past events
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ConjectureA conclusion that you reach based on inductive reasoning
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CounterexampleAn example that shows your conjecture is false
It only takes one counterexample to prove your conjecture false
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ExamplesFind the next three terms of each sequence.
11.2, 9.2, 7.2, …….1, 3, 7, 13, 21, …….
……..
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POINTS, LINES AND PLANES
Section 1-2
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PointA basic unit of geometry
Has no sizeNamed using capital letters
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LineA series of points that extends without end in two directions.
Named with a single lowercase letter or by two points on the line
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Collinear and Noncollinear
Points that lie on the same line
Points that do not lie on the same line
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RayHas a definite starting point and extends without end in one direction
Starting point is called the endpoint
Named using the endpoint first, then another point
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Line SegmentHas a definite beginning and end
Part of a line Named using endpoints
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Plane
A flat surface that extends without end in all directions
Named with a single uppercase script letter or three noncollinear points
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Coplanar and Noncoplanar
Points that lie in the same plane
Points that do not lie in the same plane
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POSTULATES
Section 1-3
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PostulatesFacts about geometry that are accepted as true
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Postulate 1-1
Two points determine a unique line
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Postulate 1-2If two distinct lines intersect, then their intersection is a point.
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Postulate 1-3Three noncollinear points determine a unique plane.
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Postulate 1-4If two distinct planes intersect, then their intersection is a line.
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CONDITIONAL STATEMENTS AND THEIR CONVERSES
Section 1-4
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Conditional StatementWritten in if-then formExamples:If points are collinear, then they lie on the same line.
If a figure is a triangle, then it has three angles.
If two lines are parallel, then they never intersect.
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HypothesisThe part following the if
If points are collinear, then they lie on the same line.
If a figure is a triangle, then it has three angles.
If two lines are parallel, then they never intersect.
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ConclusionThe part following the then
If points are collinear, then they lie on the same line.
If a figure is a triangle, then it has three angles.
If two lines are parallel, then they never intersect.
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ConverseA conditional statement is formed by exchanging the hypothesis and the conclusion in a conditional statement
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Example
Statement: If a figure is a triangle, then it has three angles.
Converse: If a figure has three angles, then it is a triangle.
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A PLAN FOR PROBLEM SOLVING
Section 1-6
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PerimeterThe distance around a figure
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FormulaAn equation that shows how certain quantities are related
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AreaThe number of square units needed to cover the surface of a figure