Can a Line Be Parallel to Itself?

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A line can indeed be parallel to itself, as parallelism is a reflexive property and an equivalence relation. This means that any line maintains a parallel relationship with itself. The discussion emphasizes the importance of understanding the definition of "parallel" to grasp this concept. Overall, the conclusion is that self-parallelism is a fundamental aspect of geometric principles. Understanding this can clarify misconceptions about parallel lines.
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Can a line be parallel to itself?
 
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Welcome to PF;
... to answer your question, 1st write down the definition of "parallel".
 
Ajit Kumar said:
Can a line be parallel to itself?

Yes, every line is parallel to itself.
 
parallelism is reflexive and is an equivalence relation.
 
thanks for your answers
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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