Is there a form of non-Euclidean geometry in which perpendicular lines never cross, or cross twice or something?

yasusar0 2022-07-15 Answered
Is there a form of non-Euclidean geometry in which perpendicular lines never cross, or cross twice or something?
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Steven Bates
Answered 2022-07-16 Author has 15 answers
Perpendicular lines are by definition those that meet at a right angle. Hence "never cross" is impossible. Non-Euclidean geometries are those that differ in the variation of the parallel postulate; especially, it holds in all of them that two distinct points determine a line so that "cross twice" is also impossible.
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The result of an isometry upon a figure containing a right angle preserves the right angle as a right angle on surface A.

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What two surfaces individually violate the first postulate and violate the fourth postulate?

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