Questions: If two lines in space do not meet, they must be parallel.

If two lines in space do not meet, they must be parallel.
Transcript text: If two lines in space do not meet, they must be parallel.
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Solution

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Solution Steps

The statement is false. In three-dimensional space, two lines that do not meet are either parallel or skew. Skew lines are lines that do not intersect and are not parallel because they are not in the same plane.

Step 1: Understanding the Statement

The statement claims that if two lines in space do not meet, they must be parallel. In three-dimensional geometry, this is not necessarily true. Lines that do not intersect can either be parallel or skew.

Step 2: Definitions
  • Parallel Lines: Lines that run in the same direction and never meet, remaining equidistant from each other.
  • Skew Lines: Lines that do not intersect and are not parallel, meaning they are not in the same plane.
Step 3: Conclusion

Since the statement does not account for the possibility of skew lines, it is incorrect. Therefore, the answer to the question is that the statement is false.

Final Answer

\(\boxed{\text{False}}\)

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