Rafael wrote the statements shown in the chart.


Statement 1 Description If a point lies outside a line, then exactly one plane contains both the line and the point.

Statement 2 Description If two points lie in a plane, then the line joining them lies in that plane.

Which option best classifies Rafael’s statements?

Answer
A:Statement 1 and Statement 2 are theorems because they can be proved.
B:Statement 1 and Statement 2 are postulates because they are true facts.
C:Statement 1 is a theorem because it can be proved and Statement 2 is a postulate because it is a true fact.
D:Statement 1 is a postulate because it is a true fact and Statement 2 is a theorem because it can be proved.

i have 12 inches mate

The correct answer is:

C: Statement 1 is a theorem because it can be proved, and Statement 2 is a postulate because it is a true fact.

To classify Rafael's statements, we need to understand the difference between theorems and postulates.

A postulate, also known as an axiom, is a statement that is accepted as true without proof. It serves as the foundation for further mathematical reasoning and can be thought of as a basic or fundamental assumption.

On the other hand, a theorem is a statement that has been proven using logical reasoning and previously established postulates and theorems.

Now let's analyze Rafael's statements:

Statement 1: "If a point lies outside a line, then exactly one plane contains both the line and the point."

This statement describes a relationship between a point, a line, and a plane. It provides a logical connection between these elements and can be proved based on previously accepted postulates and theorems. Therefore, Statement 1 is a theorem.

Statement 2: "If two points lie in a plane, then the line joining them lies in that plane."

This statement establishes a relationship between points and a line in a plane. It is a straightforward statement of fact that holds true without the need for any proof. Therefore, Statement 2 is a postulate.

Based on the analysis above, the correct classification for Rafael's statements is option C: "Statement 1 is a theorem because it can be proved, and Statement 2 is a postulate because it is a true fact."

Rafael wrote the statements shown in the chart below: