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Inductive reasoning
method used for drawing conclusions from a limited set of observations. General----> Specific
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deductive reasoning
logic to draw conclusions from statements already accepted as true.
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point
- -zero dimensions
- -has locations only
- -capital letter (A,B,C)
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line
- straight path with no thickness (one dimension)
- infinite number of points
- extended without end in both directions
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line segment
part of a line thats bounded by two end points
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plane
- flat unbounded (infinite) surface with no thickness
- two dimensional
- represented by a parallelogram
- capital letter in corner
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colinear
points contained by the same line
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coplaner
points that contained in the same plane
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noncollinear
points not on a single line
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concurrent
lines that contain a common point
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ray
- part of a line that extends endlessly in one direction
- name using endpoints first
- symbol points to the right
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angle
- a pair of rays that share the same endpoint
- sides: rays
- vertex common endpoint
- name using 3 points
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polygon
- lies in a plane
- bounded by line segments
- two dimensional
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polyhedron
- lies in space
- bounded by polygons (no curves)
- three dimensional
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perimeter
- sume of the lengths of its sides
- measured in units
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area
surface included in square units or units2
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circle
set of all points that are a fixed distance or radius from a given point in the plane.
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constructions
created with straightedge and compass
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bisect
to divide into two equal parts
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quadrilateral formula
A= 1/4(a+c)(b+d)
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conditional statements
consists of two clauses, one which begins with the word "if" or "when" or some equivalent word
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hypothesis
the letter a or "if"
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conclusion
the letter b or "then"
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Euler diagram
uses circles to illustrate how conditional statements relate to each other
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converse
statement found by interchanging the hypothesis and conclusion of the conditional statement
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contrapositive
statement formed by interchanging the a and b and denying both
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inverse
formed by denying both a and b
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syllogism
- an argument in the from
- a--> b
- b--> c
- a-->c
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Direct Proof
argument of syllogism
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premises
statements of the arguement
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conclusion
conncets the first to the last
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theorem
statement that is proved by reasoning deductively from already accepted statements
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Indirect proof
assumption made at the beginning that leads to a contradiction. The contradiction indicates that the assumption is false and the desired conclusion is true
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circularity
impossible to define everything without going around in circles
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postulate
statement assumed to be true without proof
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"determine"
if there are two points, then there is exactly one line that contains them
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Pythagorean Theorem
- a2+b2= c2
- (must be a right angle)
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Triangle Sum Theorem
the sum of the angles of a triangle is 180o
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Circle Theorems
- if the diameter of a circle is d, its circumference is pi-d
- If the radius of a circle is r, its area is pi-r2
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