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No. Normally, two lines will uniquely identify a plane, unless they happen to be parallel. If you add a third line, it will usually not be in the same plane.
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Not quite. Two lines that meet will uniquely identify a plane. But you can have lines that are neither coplanar nor parallel.
For example, consider a cube and think of the line defined by the front bottom and one of the back verticals. Neither parallel, nor coplanar.
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What is a counterexample for three coplanar lines always make a triangle?
If at least two of the three lines are parallel, the three lines will not form a triangle.
Are parallel lines always sometimes never coplanar?
They are ALWAYS coplanar! This is because the definition says so! You have to read it first, in order to get the answer!
Are non-coplanar lines skew?
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.
A line and a point not on the line are never coplanar?
No, they always are From Wikipedia.org, "The World's Encyclopedia" when I searched coplanar In geometry, a set of points in space is coplanar if the points all lie in the same geometric plane. For example, three distinct points are always coplanar; but four points in space are usually not coplanar. Since 3 points are always coplanar. A point and line are always coplanar
4 points are always coplanar?
Three points are, but not four.
