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Proposition: Prop. 11.10: Two Lines Meeting which are Parallel to Two Other Lines Meeting contain Equal Angles

(Proposition 10 from Book 11 of Euclid's “Elements”)

If two straight lines joined to one another are (respectively) parallel to two straight lines joined to one another, (but are) not in the same plane, then they will contain equal angles.

• For let the two straight lines joined to one another, $AB$ and $BC$, be (respectively) parallel to the two straight lines joined to one another, $DE$ and $EF$, (but) not in the same plane.
• I say that angle $ABC$ is equal to (angle) $DEF$.

Modern Formulation

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Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1 2

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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