Geometry Chapter 3

Question 1

Space

Answer 1

Space is the set of all points

Question 2

Collinear

Answer 2

A set of points is collinear if there is line which contains all the points of the set

Question 3

Coplanar

Answer 3

A set of points is coplanar if there is a plane which contains all of a set

Question 4

Postulate 4

Answer 4

The Line Postulate

Question 5

State the Line Postulate

Answer 5

For every two different points there is exactly one line that contains both points

Question 6

Theorem 3-1

Answer 6

If two different lines intersect, their intersection contains only one point

Question 7

Exactly one? Only One?

Answer 7

1. 1 or 0

Question 8

Postulate 5

Answer 8

The Plane Space Postulate

Question 9

State the Plane Space Postulate

Answer 9

A) Every plane contains at least 3 different non-collinear points
B) Space contains at least 4 different non-coplanar points

Question 10

Postulate 6

Answer 10

The Flat Plane Postulate

Question 11

State the Flat Plane Postulate

Answer 11

If 2 points of a line lie in a plane, then the line lies in the same plane

Question 12

Theorem 3-2

Answer 12

If a line intersects a plane not containing it, then their intersection contains only one point

Question 13

Postulate 7

Answer 13

The Plane Postulate

Question 14

State the Plane Postulate

Answer 14

Any three points lie in at least one plane, and any three non-collinear points lie in exactly one plane

Question 15

Theorem 3-3

Answer 15

Given a line and a point not on the line, there is exactly one plane containing both

Question 16

Theorem 3-4

Answer 16

Given two intersecting lines, there is exactly one plane containing both

Question 17

Postulate 8

Answer 17

Intersection of Planes Postulate

Question 18

State the Intersection of Planes Postulate

Answer 18

If two different planes intersect, then their intersection is a line

Question 19

Convex

Answer 19

A set M is called convex if for every two points P and Q of the set, the entire segment (line on top PQ) lies in M

Question 20

Postulate 9

Answer 20

The Plane Separation Postulate

Question 21

State the Plane Separation Postulate

Answer 21

Given a line and a plane containing it. The points of the plane that do not lie on the line form two sets such that
1) each of the sets is convex, and
2) if P is in one of the sets and Q is in the other, then the segment (line PQ) intersects the line

Question 22

State the Plane Separation Postulate

Answer 22

Given a line and a plane containing it. The points of the plane that do not lie on the line form two sets such that
1) each of the sets is convex, and
2) if P is in one of the sets and Q is in the other, then the segment (line PQ) intersects the line

Question 23

Half planes pt 1

Answer 23

Given a line L and a plane E containing it, the two sets described in the Plane Separation Postulate are called half planes or sides of L, and L is called the edge of each of them.

Question 24

Half planes pt2

Answer 24

If P lies in one of the half planes and Q lies in the other, then we say that P and Q lie on opposite sides of L

Question 25

Half planes pt 1 and 2

Answer 25

Given a line L and a plane E containing it, the two sets described in the Plane Separation Postulate are called half planes or sides of L, and L is called the edge of each of them. If P lies in one of the half planes and Q lies in the other, then we say that P and Q lie on opposite lines of L

Question 26

Postulate 10

Answer 26

The Space Separation Postulate

Question 27

State the Space Separation Postulate

Answer 27

The points of space that do not lie in a given plane for two sets such that 1) each of the sets is convex, and 2) If P is in one of the sets and Q is in the other, then the segment (line on top PQ) intersects the plane

Question 28

Half spaces

Answer 28

If two sets described in the Space Separation Postulate are called half spaces, and the given plane is called the fact of each of them