Notes

Undefined terms.

Point, Line, Plane
DEFINITION
betweenness A condition of one point being between two other points on a line.
bisector A line or segment that intersects a segment at its midpoint.
collinear Occurring on the same line.
coplanar Occurring on the same plane.
length of a segment The distance between the endpoints of a segment.
line segment The set of two different endpoints and all points between them.
midpoint of a segment The point on a segment that divides the segment into two equal segments.
opposite rays and are opposite rays if A, B, and C are collinear
and B (the endpoint of both rays) is between A and C.
ray A ray, is the set of all points beginning at point A and going infinitely in
the direction of point B.
space The set of all possible points.
Postulates
Postulate 1: A line contains at least two points
Postulate 1a: A plane contains at least three points not all on one line
Postulate 1b: Space contains at least four points not all in one plane.
Postulate 2: Through any two different points, exactly one line exists.
Postulate 3: Through any three points that are not on one line, exactly one plane exists.
Postulate 4 If two points lie in a plane, the line containing them lies in that plane.
Postulate 5 If two planes intersect, then their intersection is a line.
Theorems
Theorem 1-1 If two lines intersect, then their intersection is exactly one point.
Theorem 1-2 Exactly one plane contains a given line and a given point not on the line.
Theorem 1-3 If two lines intersect, then exactly one plane contains both lines.