Question

use the diagram to explain why the diagram has an example of the following postulates

1. the two - point postulate
2. line - point postulate
3. plane point postulate
4. plane intersection postulate

Explanation:

Step1: Explain two - point postulate

The two - point postulate states that through any two points, there is exactly one line. In the diagram, points A and B exist. There is exactly one line \(l\) that passes through points A and B.

Step2: Explain line - point postulate

The line - point postulate states that a line contains at least two points. Line \(l\) contains points A and B, fulfilling this postulate.

Step3: Explain plane - point postulate

The plane - point postulate states that if two points lie in a plane, then the line containing them lies in the plane. Points A and B lie in plane P, and line \(l\) which contains A and B also lies in plane P.

Step4: Explain plane intersection postulate

The plane intersection postulate states that if two planes intersect, then their intersection is a line. Planes P and Q intersect, and their intersection is line \(k\).

Answer:

1. Points A and B have exactly one line \(l\) passing through them, satisfying the two - point postulate.
2. Line \(l\) contains at least two points (A and B), satisfying the line - point postulate.
3. Points A and B in plane P mean line \(l\) (containing A and B) is in plane P, satisfying the plane - point postulate.
4. Planes P and Q intersect at line \(k\), satisfying the plane intersection postulate.