Question

Distinguish between the following statements. Which statement is the best example of a postulate?

Statement #1: A line contains at least two points.

Statement #2: All right angles are equal.

Statement #3: a+b=b+a

Answer 1

To distinguish between the statements and identify which one is the best example of a postulate, let's review each statement:

1. **Statement #1: A line contains at least two points.**
This statement is a foundational concept in geometry. It describes the basic properties of a line, and it is generally accepted to be true without needing proof.

2. **Statement #2: All right angles are equal.**
This statement is a property that can be proven and is built upon definitions in geometry. It is a theorem rather than a postulate because it requires justification based on earlier axioms or postulates.

3. **Statement #3: a + b = b + a.**
This statement is known as the commutative property of addition. Like Statement #2, it is a property that can be proven and typically derived from the axioms of arithmetic.

Based on these analyses, **Statement #1: A line contains at least two points** is the best example of a postulate. It is a basic assumption in geometry that does not require proof and serves as a foundational truth in the study of lines and geometry.