Question

Rafael wrote the statements shown in the chart below: Statement Description 1 If a point lies outside a line, then exactly one plane contains both the line and the point. 2 If two points lie in a plane, then the line joining them lies in that plane. Which option best classifies Rafael's statements? a Statement 1 is a theorem because it can be proved, and Statement 2 is a postulate because it is a true fact. b Statement 1 and Statement 2 are postulates because they are true facts. c Statement 1 is a postulate because it is a true fact, and Statement 2 is a theorem because it can be proved. d Statement 1 and Statement 2 are theorems because they can be proved.

Answer 1

Answer:

The correct option is A.

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

Step-by-step explanation:

The first statement is:

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

It is a theorem. A theorem is a statement that can be demonstrated to be true by using operations and facts that were already known.

Second statement states that:

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

It is a postulate. A postulate is a statement which is also known as axiom which is taken to be true without any proof. Theorems and Lemmas are derived from it.

Therefore the correct option is A.

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