### 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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