Lines are parallel, if they do not intersect' is stated in the form of

Options

A. an axiom
B. a definition
C. a postulate
D. a proof

Explanation

To determine the form in which the statement "Lines are parallel if they do not intersect" is stated, we can analyze the options provided: axiom, definition, postulate, and proof.

### Step-by-Step Solution:

1. **Understanding the Statement**:
The statement claims that if two lines do not intersect, then they are parallel. This is a specific condition that defines what it means for lines to be parallel.

2. **Identifying the Nature of the Statement**:
- An **axiom** is a statement that is accepted as true without proof. It is a fundamental principle.
- A **definition** is a statement that explains the meaning of a term or concept. It provides clarity on what the term entails.
- A **postulate** is a statement that is assumed to be true for the sake of argument or reasoning, often used in the context of geometry.
- A **proof** is a logical argument demonstrating the truth of a statement based on previously established statements.

3. **Analyzing the Options**:
- The statement "Lines are parallel if they do not intersect" provides a clear criterion for identifying parallel lines. It does not require proof, as it is a straightforward definition of parallel lines.
- It is not an axiom because it does not serve as a foundational truth; it is more specific.
- It is not a postulate because it does not involve an assumption made for reasoning.
- It is not a proof since it does not demonstrate the truth of a statement based on other truths.

4. **Conclusion**:
The statement is best categorized as a **definition** of parallel lines. It clearly defines what it means for lines to be parallel based on their intersection properties.

### Final Answer:
The statement "Lines are parallel if they do not intersect" is stated in the form of a **definition**.