Postulates and Theorems

Question 1

Postulate 1

Answer 1

Ruler Postulate- The distance between any 2 points equals the absolute value of difference of their coordinates.

Question 2

Postulate 2

Answer 2

Segment Addition Postulate: If B is between A and C, AB+BC=AC

Question 3

Postulate 3

Answer 3

Through any two points, there is only one line.

Question 4

Postulate 4

Answer 4

Angle Addition Postulate: If B lies in the interior of AOC, then (measure of angle AOB)+(Measure of angle BOC) = Measure of angle AOC

Question 5

Postulate 5

Answer 5

A line contains at least two points, a plane contains at least three points not all in one line, and space contains at least 4 points, not all in one plane.

Question 6

Postulate 6

Answer 6

Through any 2 points there is exactly 1 line.

Question 7

Postulate 7

Answer 7

In any three points there is at least one plane, and through any three noncollinear points, there is exactly one point.

Question 8

Postulate 8

Answer 8

If two points are in a plane, then the line containing them is also in the plane.

Question 9

Postulate 9

Answer 9

If two planes intersect, their intersection is a line.

Question 10

Theorem 1.1

Answer 10

If two lines intersect, they intersect at exactly at one point;

Question 11

Theorem 1.2

Answer 11

Through a line and a point not on the line, there is exactly one plane. (Go back to postulate 7- any three noncollinear points make exactly one plane.

Question 12

Theorem 1.3

Answer 12

If two lines intersect, then exactly one plane contains the lines. (Revisit postulate 7- through any three noncollinear points, there is exactly one plane.)