What are the signs of parallelism of straight lines?

There are only 3 of them.
If at the intersection of two straight secant the inner cross lying angles are equal, then the straight lines intersected by this secant are parallel.
If at the intersection of two straight secant the corresponding angles are equal, then the straight lines intersected by this secant are parallel.
If at the intersection of two straight secant the one-sided angles add up to 180 °, then the straight lines intersected by this secant are parallel.



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