BJU 1.11.5 Geometry
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SETS
 A collection of elements
 List method: P={red, blue, yellow}
 Set Builder Notation: P={x l x is a primary color}

ELEMENT
E symbol= "is an element of"
V={8,9,10}
9 E V

EQUIVELENT SETS
sets that have the same # of elements

EQUAL SETS
sets that are identicle

SUBSET
C = if set A contains set B.... B
c A

PROPER SUBSET
 a proper subset is a subset that is not the set itself.
 OR, two sets cannot be equal.

BINARY AND UNARY
 Has to do with 2 sets....
 Has to do with 1 set.

UNION
U= The combo of two sets

INTERSECTION
n= The common elements of two sets

DISJOINT SETS
 two sets with nothing in common
 (empty set symbol of slashed circle)

COMPLEMENT
all of the elements NOT given in a set
 u={xlx E colors}
 P={xlx E primary}
 SO.... P'={xlx "slashed element sign" primary}

Collinear Points
points that lie on the same line

NONCOLLINEAR POINTS
points that do not lie on the same line

CONCURRENT LINES
lines that intersect at a single point

COPLANAR POINTS
points that lie on the same plane

COPLANAR LINES
Lines that lie on the same plane

PARRALLEL LINES
coplanar lines that do NOT intersect

SKEW LINES
lines that are NOT coplanar

PARALLEL PLANES
planes that do NOT intersect

POSTULATE
basic statements from which the theorems are proved

THEOREM
a statement that can be logically proved using a DEFINITION, POSTULATE, or PREVIOUSLY PROVED THEOREM.

EXPANSION POSTULATE
 a line contains at least 2 points;
 a plane contains at least 3 noncollinear points;
 space contains at least 4 noncoplanar points.

LINE POSTULATE
any 2 points in space lie in exactly 1 line

PLANE POSTULATE
3 noncollinear points lie in exactly one plane

FLAT PLANE POSTULATE
 if 2 points lie in a plane,
 then the line containing these 2 points lie in the same plane

PLANE INTERSECTION POSTULATE
if 2 planes intersect, than their intersection is exactly 1 line

THEOREM 1.1
 if any 2 distinct lines intersect,
 they intersect at one & only one point.

THEOREM 1.2
a line & a point not on that line are contained in one & only one plane

THEOREM 1.3
2 intersecting lines are contained in one & only one plane

THEOREM 1.4
2 parallel lines are contained in one & only one plane