They are ALWAYS coplanar! This is because the definition says so! You have to read it first, in order to get the answer!
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Not necessarily. The Tropic of Cancer, and the Tropic of Capricorn, imaginary lines on the surface of the earth (an approximate sphere), are parallel but they are not coplanar. You could draw similar lnes on a proper sphere that were parallel but not coplanar.
No, non-coplanar lines are not skew. Skew lines are non-coplanar lines that do not intersect and are not parallel. Non-coplanar lines are simply lines that do not lie in the same plane. Skew lines, on the other hand, are non-coplanar and not parallel, making them a specific subset of non-coplanar lines.
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If at least two of the three lines are parallel, the three lines will not form a triangle.
Two coplanar lines that never intersect are called called parallel lines.