Unit Two- Postulates And Theorems

Question 1

Space

Answer 1

The set of all points

Question 2

Collinear

Answer 2

A set of points is collinear if there is a line containing all the points of the set

Question 3

Postulate 4- The Line Postualte

Answer 3

For every two different points there is exactly one line containing both points.

Question 4

If two different lines intersect…

Answer 4

…there intersection contains only one point.

Question 5

Postulate 5- The Plane Space Postulate

Answer 5

a) Every plane contains at least three different non collinear points.
b) Space contains at least four different non coplanar points.

Question 6

Postulate 6- The Flat Plane Postulate

Answer 6

If two points of a line lie on a plane, then the line lies in the same plane.

Question 7

If a line intersects a plane not containing it…

Answer 7

…then the intersection contains only one point.

Question 8

Postulate 7- Plane Postulate

Answer 8

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

Question 9

Given a line and a point not on the line…

Answer 9

…there is exactly one plane containing both.

Question 10

Given two intersecting lines…

Answer 10

…there is exactly one plane containing both lines.

Question 11

Postulate 8- Intersection of Planes Postulate

Answer 11

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

Question 12

Postulate 9- The Plane Separation Postulate

Answer 12

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 PQ intersects the line.

Question 13

Postulate 10- The Space Separation Postulate

Answer 13

The points of space that do not lie in a given plane form two sets, such that…

1) each of the sets is convex, and
2) If P is one of the sets and Q is in the other, then the segment PQ intersects the plane.