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Postulate 5

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

Postulate 6

Through any two points there is exactly one line

Postulate 7

Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.

Postulate 8

If two points are in a plane, then the line that contains the points is in that plane

Postulate 9

if two planes intersect, then their intersection is a line

Theorem 1-1

if two lines intersect, then they intersect in exactly one point

Theorem 1-2

Through a line and a point not in the line there is exactly one plane.

Theorem 1-3

If two lines intersect, then exactly one plane contains the lines.

Segment

Two points on a line and all points in between them.

Ray

all points on segment AC and all points P such that c is between A and P

Opposite Rays

given 3 collinear points R,S,T,- if S is between R and T, SR and ST are opposite Rays

Length

Distance Between Endpoints of a Segment.

Ruler Postulate

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

Congruent

Having the same size and shape

Congruent Segments

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

Congruent Angles

Angles that have equal measures

Adjacent Angles

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.