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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.

• For let the two straight lines $AB$ and $CD$ be at right angles to a reference plane.
• I say that $AB$ is parallel to $CD$.

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

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References

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

1. Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016