Which of the following statements are true and which are false ?
If two line segments do not intersect, they are parallel.

Answer

To determine whether the statement "If two line segments do not intersect, they are parallel" is true or false, we can follow these steps:

### Step 1: Understand the Definition of Parallel Lines
Parallel lines are defined as lines in a plane that do not meet; they are always the same distance apart and will never intersect, no matter how far they are extended.

**Hint:** Remember that parallel lines maintain a constant distance from each other.

### Step 2: Analyze the Statement
The statement claims that if two line segments do not intersect, they must be parallel. This means that if we find two line segments that do not intersect but are not parallel, the statement would be false.

**Hint:** Consider whether there are situations where two lines do not intersect but are not parallel.

### Step 3: Create an Example
Let's visualize two line segments.
- Let line segment AB be horizontal.
- Let line segment CD be diagonal and positioned above line segment AB.

In this case, line segment AB does not intersect with line segment CD, but they are not parallel because they are at different angles.

**Hint:** Draw a diagram to see how two lines can be positioned without intersecting.

### Step 4: Conclusion
Since we found an example where two line segments do not intersect but are not parallel, we conclude that the statement "If two line segments do not intersect, they are parallel" is false.

**Hint:** Always check with examples to verify mathematical statements.

### Final Answer
The statement is **False**.