Ch. 1.5 | An Ideal Euclidean Model

Question 1

Complete

Answer 1

Every statement that can be expressed within the system can be proved or disproved from the postulates.

Question 2

Consistent

Answer 2

“Consistent” Postulate - systems contain postulates that do not contradict one another.

Question 3

Incidence Postulates

Answer 3

The first five postulates in the system of geometry. The entire structure of geometry is built on these postulates.

Question 4

Independent

Answer 4

“Independent” Postulate - system in which no postulate can be deduced or proved from the other postulates in the system.

Question 5

Postulate 1.1 | Expansion Postulate

Answer 5

A line contains at least two points. A plane contains at least three noncollinear points. Space contains at least four noncoplanar points.

Question 6

Postulate 1.2 | Line Postulate

Answer 6

Any two points in space lie in exactly one line.

Question 7

Postulate 1.3 | Plane Postulate

Answer 7

Three distinct noncollinear points lie in exactly one plane.

Question 8

Postulate 1.4 | Flat Plane Postulate

Answer 8

If two points lie in a plane, then the line containing these two points lies in the same plane.

Question 9

Postulate 1.5 | Plane Intersection Postulate

Answer 9

If two planes intersect, then their intersection is exactly one line.