Postulates

Question 0

What does postulate 1.2 state?

Answer 0

Any two points in space lie in exactly one line

Question 1

What does postulate 1.1 state? (The Expansion postulate)

Answer 1

A line contains at least two points. A plane contains at least three non collinear points. Space contains at least four non coplanar points

Question 2

What does postulate 1.3 state?

Answer 2

Three distinct non collinear points lie in exactly one plane

Question 3

What does postulate 1.4 state?

Answer 3

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

Question 4

What does postulate 1.5 state?

Answer 4

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

Question 5

What does postulate 2.1 state?

Answer 5

Every point divides any line through that point into three disjoint sets: the point and two half lines

Question 6

What does postulate 2.2 state? (Plane Separation)

Answer 6

Every line divides any plane containing the line into three disjoint sets: the line and two half-planes

Question 7

What does postulate 3.1 state?

Answer 7

The ruler postulate: every point of a line can be placed in correspondence with a real number

Question 8

What does postulate 3.2 state?

Answer 8

The completeness postulate: given a ray AB and any positive real number r, there is exactly one point C on the ray so that AC=r

Question 9

Postulate 4.1

Answer 9

Protractor postulate: for every angle A there corresponds a positive real number less than or equal to 180

Question 10

Postulate 4.2

Answer 10

Continuity postulate: if k is a half plane determined by AC then for every real number there is exactly one Ray AB that lies in k