WEBVTT
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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.
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There are two key facts about two skew lines in three-dimensional geometry.
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The first is that they do not intersect.
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As the lines do not intersect, this immediately rules out option C and option D, as option C stated they have a common point.
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Option D stated that they intersect.
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This leaves us with options A, B, and E.
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The second key fact about two skew lines is that they are not parallel.
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This rules out option B, which stated that they were parallel.
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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.
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Any two lines that are in the same plane and do not intersect must be parallel.
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Therefore, option E cannot be true.
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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.