Question

Rafael wrote the statements shown in the chart.

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.

Answer 1

The correct answer is A

Answer 2

The correct option that best classifies Rafael's statement is:

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

Explanation:

" We know that a postulate also known as a axiom is a statement that is considered to be true and does not need any kind of proof "

" Whereas a theorem is a statement that need to be derived with the help of corollaries or axioms or some statements "

Hence, we are given two statements as:

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

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

So, statement 1 is a Theorem and statement 2 is a postulate.