Concept explainers
Determine whether the given statement is still true if the lines are not coplanar.
Explanation of Solution
Given:
Perpendicular Transversal Converse Theorem:
In a plane , if two lines are perpendicular to the same line , then they are parallel.
Calculation :
Consider the diagram :
Given :
R and S are different planes (not necessarily parallel) and l and m are lines in planes R and S respectively such that :
To Prove :
Clearly , since the two lines are perpendicular to the same line , they are parallel .
Hence the given statement holds even if the lines are not coplanar.
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