MHB What does the following means?

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The statement suggests that in Euclidean geometry, two distinct straight lines cannot share two points without being the same line. If two lines have two points in common, they must coincide entirely. This reinforces the idea that lines can either be parallel with no points in common or intersect at exactly one point. The discussion clarifies the relationship between lines and points in geometric terms. Overall, the concept emphasizes the uniqueness of straight lines in relation to their points.
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.
 

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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