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Are two lines parallel if they do not intersect?
Yes, but only if they are straight lines in the same plane.
Two lines lie in one plane if and only if the lines are parallel?
Two lines are coplanar iff they are parallel OR intersect.
Are in the same plane but do not intersect?
The only lines that are in the same plane that do not intersect are: 1. Lines of finite length (eg 1 6" line on the floor at one end of the room and another 8" line at the other end) 2. Parallel lines
If a transversal intersect two lines then the lines are parallel if and only if a pair of alternate interior angles are equal?
Yes (assuming all three lines are in the same plane).
When are skew lines coplanar?
Never! Coplanar means that the two lines lie in the same two-dimensional plane. The only way that two lines do not intersect in two-dimensional space is if they are parallel. And by definition, skew lines are not allowed to be parallel, either.So essentially there is no such thing as skew lines that only occupy two dimensions. Skew lines must be in three dimensions or higher in order to (1) not intersect and (2) not be parallel with each other.
Are two lines parallel if they do not intersect?
Yes, but only if they are straight lines in the same plane.
Two lines lie in one plane if and only if the lines are parallel?
Two lines are coplanar iff they are parallel OR intersect.
If Two lines lie in one plane and do not intersect if and only if the two lines are parallel is this true?
Yes [in the Euclidean plane].
Why is there only one kind of parallel lines?
parallel lines are any lines that will never touch. on a 3D plane, there will be many lines that won't intersect another. but parallel lines have a specific definition that there is no way to subcatigorize it
Are in the same plane but do not intersect?
The only lines that are in the same plane that do not intersect are: 1. Lines of finite length (eg 1 6" line on the floor at one end of the room and another 8" line at the other end) 2. Parallel lines
If a transversal intersect two lines then the lines are parallel if and only if a pair of alternate interior angles are equal?
Yes (assuming all three lines are in the same plane).
A and B do not intersect what information is needed to prove that they are parallel?
Pretty much the only thing you need to know to determine if two lines are parallel is the gradient of those lines. Simply put, are the lines on the same plane?
When are skew lines coplanar?
Never! Coplanar means that the two lines lie in the same two-dimensional plane. The only way that two lines do not intersect in two-dimensional space is if they are parallel. And by definition, skew lines are not allowed to be parallel, either.So essentially there is no such thing as skew lines that only occupy two dimensions. Skew lines must be in three dimensions or higher in order to (1) not intersect and (2) not be parallel with each other.
How can two noncoplanar lines intersect?
Noncoplanar lines cannot intersect because they exist in different planes and do not share a common point. However, they can be skew lines, which means they are neither parallel nor intersecting. In three-dimensional space, two lines are only able to intersect if they lie in the same plane. Therefore, it is geometrically impossible for two noncoplanar lines to intersect.
Do parallel lines have to be on the same plane?
Yes. Parallel means they they are always the same distance and they never intersect, and this could only mean on the same plane. However, the proof that it works is a little harder than one might think.
How many Counterexamples are needed to disprove the conjecture two lines in a plane always intersect at exactly one point?
To disprove the conjecture that two lines in a plane always intersect at exactly one point, only one counterexample is needed. A single example of two lines that do not intersect, such as two parallel lines, is sufficient to show that the conjecture is false. Therefore, one counterexample is enough to invalidate the claim.
Why is the distance between two lines only defined for parallel lines?
because they never intersect
