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They are skew lines.

Two parallel lines must be in the same plane.

Q: Two lines that do not intersect and are in different planes?

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skew lines

Each line can either intersect the edge which is common to the two planes at some point or be parallel to it. If the two lines intersect the edge, but at different points, then the lines are skew. If only one of the lines intersects the edge, then again the lines are skew. If neither of them intersect, then the two lines are parallel to the same edge and so they are parallel to one another so not skew.

Two straight lines, whether they're in the same or different planes, must intersect at either one point or else at no points.

No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.

parallellines

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Two lines that are not coplaner exist on two different planes. These lines do not and will not intersect by simple definition. It is however, when speaking of three or more lines, when the possibility that two or more of them may intersect.

No.

They're either parallel lines or skew lines.

They may be either parallel or skew.

yes two lines intersect to form a point two planes intersect to form a line

Intersecting planes!

Each line can either intersect the edge which is common to the two planes at some point or be parallel to it. If the two lines intersect the edge, but at different points, then the lines are skew. If only one of the lines intersects the edge, then again the lines are skew. If neither of them intersect, then the two lines are parallel to the same edge and so they are parallel to one another so not skew.

Two straight lines, whether they're in the same or different planes, must intersect at either one point or else at no points.

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