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Geometry Review for Chapter 1

Hannah Fleming

Review of the Geometry facts learned in Chapter 1

independent to the point; no ambiguous or vague language
unaryoperations all elements in the universal set not in the given set
equivalentsets How many points are required for something to be noncollinear
set lines that intersect at a single point
proving objects of the set
equal don't contradict one another
coplanarpoints something that forces a decision apart from or in opposition to reason
consistent sets with one-to-one correspondence
theorem model based on 5 incidence postulates
null a line contains 2 points; a plane contains 3 noncollinear points; space contains 4 noncoplanar points
logic a group or collection of objects denoted by braces and labeled with a capital letter
coplanarlines points that do not lie on the same plane
clear accurate and reversible
plane are the foundation to our system of geometry
complement set that contains no elements
concurrentlines coplanar lines that do not intersect
disjointsets 3 distinct noncollinear points lie in exactly one plane
noncollinearpoints don't rely on other postulates
expansionpostulate repeat the pattern established by the last 3 elements
flatplanepostulate refers to processes that require two sets
binaryoperations points that lie in the same plane
parallellines operations on a single set
parallelplanes points that lie on the same line
collinearpoints any 2 points in space lie in exactly one line
linepostulate assumed to be true
logic what makes a good geometry
objective if 2 planes intersect, then their intersection is exactly one line
line denoted by "U"
universalset when two sets have nothing in common
three flat, extends infinitely in two dimensions
ellipse sets with the exact same elements
skewlines another name for a postulate
useful straight; extends infinitely in one direction; length, no width or thickness
point a system of definitions, postulates, and theorems that is built in a logical progression
complete a visual representation of sets
incidencepostulates good grammar, good sentence, only necessary words
Euclideanmodel spot; no dimension; a location in space
axiom lines that lie in the same plane
elements planes in space that do not intersect
planeintersectionpostulate lines that are not coplanar
planepostulate using words previously defined or commonly accepted as undefined
concise process of justifying a theorem
precise interrelation or sequence of facts or events when seen as inevitable or predictable
goodpostulate neutral; avoids limitations of time or place
geometry a statement that can be shown to be true by a logical progression of previous terms and statements
Venndiagram doesn't rely on anything but postulates
postulate if 2 points lie in a plane, then the line containing these 2 points lies in the same plane

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