Prove that two lines in a plane which are perpendicular to the same given line in the plane are parallel to each other.
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If two lines cross a third line in such a manner that the sum of the interior angles is 180∘ then the lines are parallel. If two lines are perpendicular to the same plane then a line through the two points of intersection with the plane will form a 90∘ with each of the original two lines.
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