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

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

Statement #2: All right angles are equal.

Statement #3: a+b=b+a

(1 point)
Statement #
is a postulate.

1 answer

A postulate, also known as an axiom, is a fundamental statement or assumption that is accepted without proof and serves as a starting point for further reasoning and arguments in mathematics and geometry.

Let's analyze the statements:

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

    • This is a foundational statement in geometry that describes a property of lines. It is typically accepted as true without requiring proof, making it a postulate.
  2. Statement #2: All right angles are equal.

    • This is generally accepted in Euclidean geometry as a theorem that can be proved based on the definitions and properties of angles. It is not typically classified as a postulate but rather a derived statement.
  3. Statement #3: a + b = b + a

    • This describes the commutative property of addition in arithmetic, which is also a fundamental concept that can be proved. It does not serve as a postulate for geometry itself.

Therefore, the statement that is a postulate is Statement #1: A line contains at least two points.

To answer your question:

Statement #1 is a postulate.