What does the following means?

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SUMMARY

The discussion clarifies the statement regarding the nature of straight lines in Euclidean geometry. It establishes that two distinct straight lines cannot share two points without being the same line, meaning they either do not intersect at all (parallel) or intersect at exactly one point. This conclusion is supported by the principles of Euclidean geometry, emphasizing the uniqueness of lines based on their points of intersection.

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cbarker1
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Dear Everybody,
What does the following means:
Two straight lines cannot have any two points of one coincide with two points of the other without the lines coinciding altogether?

I think it means that line can't overlap with itself.

Thanks,
Cbarker1
 
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I take that statement to mean that no two straight lines can have two points in common without being the same line (coinciding).
 
In other words, in Euclidean geometry, two distinct lines are either parallel, and have no points in common, or intersect, and have exactly one point in common.
 

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