To distinguish between the statements and identify which one is a postulate, let's analyze each statement:
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Statement #1: A line contains at least two points.
- This statement reflects a fundamental property of lines in Euclidean geometry. It is generally accepted as a basic geometric truth and is taken as a postulate in many geometric systems.
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Statement #2: All right angles are equal.
- This statement is related to the properties of angles and is typically proven as a theorem rather than taken as a postulate. It is often derived from the definitions of right angles and properties of angles in geometry.
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Statement #3: \( a + b = b + a \)
- This statement expresses the commutative property of addition in mathematics. It is a general rule concerning numbers but is not a geometric postulate.
Conclusion:
- Statement #1 is a postulate, as it establishes a foundational thought in the framework of geometry regarding lines and points.
- Statements #2 and #3 are not postulates; Statement #2 is a theorem related to angles, while Statement #3 pertains to the properties of numbers in arithmetic.
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