a line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane
Through any two points there is exactly one line
Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.
If two points are in a plane, then the line that contains the points is in that plane
if two planes intersect, then their intersection is a line
if two lines intersect, then they intersect in exactly one point
Through a line and a point not in the line there is exactly one plane.
If two lines intersect, then exactly one plane contains the lines.
Two points on a line and all points in between them.
all points on segment AC and all points P such that c is between A and P
given 3 collinear points R,S,T,- if S is between R and T, SR and ST are opposite Rays
Distance Between Endpoints of a Segment.
1. The points on a line can be paired with the real numbers in such a way that any tho points can have coordinates 0 and 1. 2. Once a coordinate system has been chosen in this way , the distance between any two points equals the absolute value of the differences of their coordinates.
Segment Addition Postulate
If B is between A and C, then AB+BC=AC
Having the same size and shape
segments that have equal lengths
Midpoint of a Segment
The point that divides the segment into two congruent segments
Bisector of a Segment
a line, segment, ray, or plane that intersects the segment at its midpoint
Angle Addition Postulate
if point B lies in the interior of <AOC then m<AOB+m<BOC=m<AOC
Angles that have equal measures
Two angles in a plane that have a common vertex and common side but no common interior points.
Bisector of an Angle
the ray that divides the angle into two congruent adjacent angles.