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Congruous DID pop into my head just before I read your reply...is that right? I'm guessing it is - thank you.
And technically yes lines are by nature unbroken, but you can have a dashed line which isn't technically congruous or you can be trying to make a line "congruous" (say, in a puzzle that requires you to make an unbroken line from separate pieces).
Congruence (congruous, congruent) is not for unbroken line. Congruence denotes same size and shape. A segment is two points on a line and all points in between. That is about the only thing I can think of off the top of my head.
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And isn't a line, by definition, unbroken?
And technically yes lines are by nature unbroken, but you can have a dashed line which isn't technically congruous or you can be trying to make a line "congruous" (say, in a puzzle that requires you to make an unbroken line from separate pieces).