BJU 1.1-1.5 Geometry

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 AA={1,2,3,4,5}B={1,2,3}

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 setu={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