Q: What- planes ABC and EFG are parallel.Which of these segments must be parallel?

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two line segments that are not parallel are intersecting even if they don't touch like this /l / l they are considered intersecting because you must extend it like they are lines to say they are parallel or not

They are skew lines. Two parallel lines must be in the same plane.

no They just have to have four sides the same length and the oppsite line segments must be parallel.

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

They are called skew lines. Explanation: In 3 space, parallel lines must never intersect AND must be in the same plane. If they fail to intersect and are in different planes we call them skew lines.

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No. By definition, planes can be extended in all directions to infinity. If they are not parallel, they will intersect somewhere.

two line segments that are not parallel are intersecting even if they don't touch like this /l / l they are considered intersecting because you must extend it like they are lines to say they are parallel or not

They are skew lines. Two parallel lines must be in the same plane.

no They just have to have four sides the same length and the oppsite line segments must be parallel.

We don't think so. We reasoned it out like this: -- Two planes either intersect or else they're parallel. -- If two planes intersect, then they're not parallel. -- In order for the third one to avoid intersecting either of the first two, it would have to be parallel to both of them. But if they're not parallel to each other, then that's not possible. If the third plane is parallel to one of the first two, then it's not parallel to the other one, and it must intersect the one that it's not parallel to.

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

They are called skew lines. Explanation: In 3 space, parallel lines must never intersect AND must be in the same plane. If they fail to intersect and are in different planes we call them skew lines.

Yes, they can. Since three points define a plane, take any two points on one line and a point on the other line, and form the plane with those three points. Once you have that, then use Euclid's test to see if they are parallel. Alternately, if the planes themselves are parallel, then the lines are as well, since they definitely will never intersect.

Technically, lines are continuous, so parallelograms are actually composed of line segments. The line segments composing the sides of the parallelogram, come in two pairs in 2D space. Each pair is composed of two line segments that are parallel to each other, but do not occupy the same line. The two pares of line segments must all meet to then form a quadrilateral.

There is a subtle distinction between Euclidean, Hilbert and Non-Euclidean planes. Euclidean planes are those that satisfy the 5 axioms, while Non-Euclidean planes do not satisfy the fifth postulate. This means that in Non-Euclidean planes, given a line and a point not on that line, then there are two (or more) lines that contain that point and are parallel to the original line. There are geometries where there must be exactly one line through that point and parallel to the original line and then there are also geometries where no such line contains that point and is parallel to the original line.Basically, the fifth postulate can be satisfied by multiple geometries.

No, as long as the lines will never touch, they are parallelNo, if they have the same slope, they're parallel. This means they could be vertical, horizontal, or anything in between.And don't listen to the other guy, because skew lines are lines on two different planes, never intersect, and are not parallel.