Chapter 3 Flashcards
The set of all points
Space
A set of points on the same line
Collinear
A set of points on the same plane
Coplanar
Every plane contains at least three different noncollinear points
Plane postulate
If two different lines intersect, their intersection contains only one point
Intersection of lines theorem
TRUE or FALSE: the intersection of two different lines is exactly one point
FALSE, can be 0 points
Space contains at least 4 noncoplanar points
Space postulate
If two points of a line lie in a plane, then the line lies in the same plane
Flat plane postulate
If a line intersects a plane not containing it, then the intersection contains only one point
Theorem 3-2
Any 3 points line in AT LEAST one plane. Any 3 NONCOLLINEAR points line in EXACTLY ONE plane.
Plane postulate
Given a line and a point not on it, there is exactly one plane containing both
Theorem 3-3
Given two intersecting lines, there is exactly one plane containing it
Theorem 3-4
If two planes intersect, then their intersection is a line
Intersection of planes postulate
For every two points, P and Q, of the set, the entire segment PQ lies within M
Convex
Given a line and a plane containing it, the points of the plane not on the line form two sets such that:
1. Each set is convex
2. If P is in one set and Q in the other, the segment PQ intersects the line
Plane separation postulate
Each convex set is called a _____. They lie on the sides of the line. The line is the edge of the ____.
Half-plane
Either of the two parts into which a plane divides the three-dimensional Euclidean space
Half-space
“opposite sides” or “opposite”
Coplanar
“Different sides”
Noncoplanar
The points of space not in a given plane form two sets such that:
1. Each set is convex
2. If P is in one set and Q the other, the segment PQ intersects the plane
Space separation postulate
If a path can be traced one and end in a different location
Euler path
Starting and ending points are the same
Euler circuit
Circuit has ____ odd vertices
0
Path has _____ odd vertices
2
Neither is _______
Neither 0 or 2 odd vertices
If we say that A, B, and C are three points, we mean that A, B, and C must be _____ points
different
If we say that L1 and L2 are lines, we allow the possibility that L1 and L2 are the _____ line
Same
two points determine a line written as AB
The line postulate
