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:
-
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.
-
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.
-
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.