1-5 Posulates and Theorems

Relating Points, Lines, & Planes

Postulates Defintion

Statement accepted w/o proof

Postulate 5

Dimension Postulate:

A line contains at least… 2 “distinct” points

A plane contains at least.. 3 ““ noncollinear points

Space contains at least… 4““ noncoplanar points

Postulate 6

Straight Line Postulate

Through any 2 distinct points there is … exactly one line

“one and only one”

Postulate 7

Plane Existence Postulate

Through any 3 distinct points there is… at least one plane

Through any 3 distinct noncollinear points there is… exactly one plane

Postulate 8

Flat Plane Postulate

If 2 distinct points are in a plane, then… the line that contains the points is also in the plane

Postulate 9

Plane Intersection Postulate

If 2 distinct planes intersect, then… their intersecton is a line

Theorems defintion

A proven statement

Theorem 1.1

Line Intersection Theorem

If 2 disinct lines intersect, then… they intersect in exactly one point

Theorem 1.2

Line-Point Theorem

If there is a line and a point not on the line, then… exactly one plane contains them

Theorem 1.3

Line Intersect-Plane Theorem

If two distinct lines intersect, then… exactly one plane contains them

Ruler Postulate

Postulate 1

1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1.

2. Once a coordinate system has been chosen this way, the distance between any two points equals the absolute value of the difference of their coordinates.

Segment Addition Postulate

Postulate 2

If B is between A and C, then: AB+BC=AC

(example on pg 13)

Angle Addition Postulate Pt. 1

Measure of angle COB+ measure of angle BOA= m < (angle) COA

Angle Addition Postulate Pt. 2

m<1+m<2=180

Congruent Segments

Same size and shape

symbol ~ above =

Midpoint of a segment

splits the segment in 2 congruent parts

Bisector of a segment

a segment, line, ray, or plane intersecting a segment @ its midpoint