Video: Planes and Straight Lines

Complete the following: Two skew lines are two lines that _. [A] do not lie in the same plane and do not intersect [B] are parallel [C] lie in the same plane and have a common point [D] intersect but do not lie in the same plane [E] lie in the same plane and do not have a common point.

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Video Transcript

Complete the following: Two skew lines are two lines that A) do not lie in the same plane and do not intersect, B) are parallel, C) lie in the same plane and have a common point, D) intersect but do not lie in the same plane, or E) lie in the same plane and do not have a common point.

There are two key facts about two skew lines in three-dimensional geometry. The first is that they do not intersect. As the lines do not intersect, this immediately rules out option C and option D, as option C stated they have a common point. Option D stated that they intersect. This leaves us with options A, B, and E.

The second key fact about two skew lines is that they are not parallel. This rules out option B, which stated that they were parallel. We’re now left with option A do not lie in the same plane and do not intersect and option E lie in the same plane and do not have a common point.

Any two lines that are in the same plane and do not intersect must be parallel. Therefore, option E cannot be true. This leaves us with our answer: option A two skew lines are two lines that do not lie in the same plane and do not intersect.

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