Proposition: Prop. 11.06: Two Lines Perpendicular to Same Plane are Parallel
(Proposition 6 from Book 11 of Euclid's “Elements”)
If two straight lines are at right angles to the same plane then the straight lines will be parallel.
Modern Formulation
In other words, If two straight lines are at right angles to the same plane then the two straight lines lie in the same plane, and never meet when produced in either direction.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2 3 4
Thank you to the contributors under CC BYSA 4.0!
 Github:

 nonGithub:
 @Fitzpatrick
References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016